Enhancing soil fertility through the application of biohumus

. The development and advancement of nonlinear mathematical models is an important task in many fields of science and engineering. Nonlinear models allow for the description and prediction of complex and nonlinear processes that cannot be fully characterized by linear equations. In biology, nonlinear models are applied to study complex biological systems such as population dynamics, interactions in ecosystems, genetic networks, and others. Nonlinear equations enable the consideration of nonlinear interactions and feedback between different components of the system. The objective of this work is to develop a system of nonlinear models for a biological population to address the task of enhancing soil fertility through the application of biohumus.


Introduction
Soil degradation processes, such as humus loss and deterioration of agrophysical properties, pose significant challenges in agriculture in many countries worldwide.Humus loss, known as humification, refers to the depletion of soil organic matter, which is essential for plant nutrition and the maintenance of soil structure and fertility.Deterioration of agrophysical properties, such as soil texture, permeability, air exchange, moisture retention, etc., can also significantly reduce crop yield and soil quality [1].
There are several reasons contributing to these degradation processes.In some cases, improper agricultural practices such as improper cultivation, unsuitable irrigation systems, excessive use of pesticides and fertilizers, can lead to the destruction of soil structure and reduction of organic matter content.This can result in soil erosion and the loss of the fertile soil layer [2].
However, there are various methods and practices available to combat soil degradation and improve agrophysical properties.Some of them include [3]: Adoption of sustainable agricultural practices, such as crop rotation, organic fertilization, composting, and green manure.These practices help preserve soil structure and increase organic matter content.
Application of Biochar and Mineral Fertilizers: According to the experimental design, apply biochar and mineral fertilizers to the respective plots.Refer to specific dosage recommendations and application methods for each material.
Sowing and Plant Care: Sow the selected plants in each plot and provide appropriate care, including watering, weed removal, and protection against pests.Regularly monitor the growth and development of the plants, collect data on yield and other parameters you wish to study.
Results Analysis: After data collection, analyze the results and determine the impact of applying biochar and mineral fertilizers on soil fertility and agrophysical properties.Use statistical methods to test the statistical significance of the obtained results.
Interpretation of the Study: Interpret the research findings, draw conclusions, and formulate recommendations for practical application.Describe the advantages and limitations of using biochar and mineral fertilizers on degraded gray-brown soils.
Publication and Dissemination of Results: Communicate the research results through publication in scientific articles, conference presentations, and information exchange with other researchers, agricultural producers, and stakeholders.
It is also important to note that conducting similar studies over an extended period is recommended to assess the long-term effects of applying biochar and mineral fertilizers on degraded gray-brown soils [1][2][3][4][5][6].

Materials and methods
The main research method is the self-similar approach [7][8][9].
In the domain consider the cross-diffusion system of convective transport equations [10]: Here: -diffusion coefficients, ( ) l t -The velocity of convective transport, where  -solution of system of equation [11].To solve the system of equations (1), we will construct a self-similar system of equations using the method of nonlinear splitting.
Then choose the parameter: Next, we come to the solution of a system of equations of the form [12]: When the condition we arrive at the following system of equations [13]: Wave solutions of system (1) are sought in the form [14]   Then we have a system: The wave solution of system (4) has the form [15]   Where c-speed of the wave.
We have The solution of system (5) will be sought in the form The results obtained in the work can be used to solve the problems of increasing soil fertility depending on the application of biohumus [21][22].

Results and Discussion
The agrochemical properties of biohumus may include: Increase in organic matter content: Biohumus is composed of decomposed organic material that contains essential nutrients for plants.Adding biohumus to the soil helps increase the organic matter content, which positively affects plant nutrition.
Adding biohumus helps increase the content of these elements in the soil, promoting better plant nutrition.
Enrichment of soil with trace elements: Biohumus can also contain various trace elements such as iron (Fe), copper (Cu), zinc (Zn), and manganese (Mn).These trace elements are necessary for normal plant growth and development, and adding biohumus can enrich the soil with them.
Enhancement of cation exchange capacity: Biohumus has a high cation exchange capacity, meaning its ability to retain and exchange cations (positively charged ions) with dissolved nutrient elements.This facilitates better uptake of nutrients by plants.
pH regulation: Biohumus can influence soil pH, especially under acidic or alkaline conditions.It can help stabilize soil pH within the optimal range for plant growth, which is an important factor for efficient nutrient utilization.The humus content is a key factor in soil fertility.Humus is the organic component of soil composed of decomposed plant and animal material.Humus contributes several positive impacts on soil fertility: Improvement of soil structure.Moisture retention: It acts as a reservoir, allowing plants to access moisture even during periods of drought.This is particularly important in regions with limited water availability.
Nutrient environment for microorganisms: Humus provides a nutrient-rich environment for microorganisms such as bacteria and fungi, which play a vital role in organic material decomposition and nutrient cycling.Microorganisms help break down organic matter, making it accessible to plants.
pH regulation: Humus contributes to pH stabilization in the soil, which is crucial for nutrient uptake by plants.It helps maintain an optimal pH level, creating conditions for normal plant functioning.Increasing the humus content in the soil is one of the strategies to enhance soil fertility and sustain agricultural production.Adding biohumus is one way to increase the humus content in the soil and improve its fertility.
Biohumus is formed through the natural process of organic material decomposition under the influence of microorganisms.During the decomposition process, organic material transforms into more accessible forms of nutrients, including water-soluble forms of nitrogen (nitrates, ammonium), phosphorus (orthophosphates), and potassium (potassium ions).Simple organic fertilizers such as compost or manure also contain some amount of these water-soluble forms of nutrients.However, the content of these forms in biohumus can be higher due to the process of its formation, which promotes more complete decomposition of organic material and the formation of available nutrients.It is known that the main factor determining soil fertility is the content of humus.The results of conducted research have shown the minimum humus content under control conditions without fertilization to be 2.31%.The application of biohumus at a rate of 3 tons per hectare + N 60 K 60 resulted in a humus content of 2.64%.Biohumus at a rate of 4 tons per hectare + N 30 K 30 led to a humus content of 2.82%.Biohumus at a rate of 5 tons per hectare + N 30 resulted in a humus content of 2.93%.The addition of 4 tons of biohumus contributed to an increase in this indicator by 0.62%.
Biohumus is a valuable, environmentally friendly organic fertilizer.The application of biohumus, obtained through vermicomposting, increases the humus content in the soil, thus enhancing its fertility.
Changes observed in humus content, agrochemical composition, and agrophysical properties of the soil when biohumus is applied together with mineral fertilizers may result from the interaction of these components and their influence on soil processes.Here are some general research findings related to this issue: Humus content: The application of biohumus and mineral fertilizers can contribute to an increase in humus content in the soil.Biohumus contains organic substances that can serve as a source of nutrients for soil microorganisms, improve soil structure, and promote humus formation.
Agrochemical composition: The application of biohumus and mineral fertilizers can affect the content of nutrients in the soil, such as nitrogen, phosphorus, potassium, and other macro-and micronutrients.Biohumus may contain a certain amount of nutrients that can gradually release and become available to plants.
Agrophysical properties: The application of biohumus and mineral fertilizers can influence the physical properties of the soil, including structure, moisture, air exchange, water retention, and permeability.Biohumus can contribute to improving soil structure, enhancing its water-holding capacity, and improving agrophysical conditions for plant root systems.
Research results may vary depending on the composition and dosage of the applied materials, soil type, climatic conditions, and other factors.To obtain more accurate and generalized results, it is necessary to conduct numerous studies under different conditions and regions.
The interpretation of these results should take a comprehensive approach into account and also consider ecological, economic, and social factors.
The impact of biohumus and mineral fertilizers on soil depends on their composition, dosage, and ratio.Results may vary depending on soil type, climatic conditions, cultivated crops, and other factors.This emphasizes the need for more detailed research to determine the optimal conditions for applying biohumus and mineral fertilizers to achieve the best results in improving soil fertility.
Research confirms the multifaceted positive impact of biogas on the agrochemical, agrophysical, and biological characteristics of soil.Here are some valuable properties of biogas: Water Holding Capacity: Biogas has high water holding capacity, meaning it can retain and preserve moisture in the soil.This is particularly important in dry and semi-arid regions where water availability is a limiting factor for plants.
Water Resistance: Biogas has the ability to maintain its water holding capacity even during prolonged dry periods or intense irrigation.This helps sustain soil moisture levels over an extended period.
Hydrophilicity: Biogas improves soil permeability to water, facilitating water infiltration and dispersion throughout the soil profile.It prevents surface runoff and soil erosion.
Absence of Weed Seeds: Biogas is typically subjected to specialized processing, which eliminates or significantly reduces the presence of weed seeds.This reduces weed-related problems in crops and enhances their quality.
Biogas also contributes to improving the biological activity of soil, stimulating the growth and development of soil microorganisms, enhancing the biological availability of nutrients to plants, and promoting soil biodiversity.
All these properties make biogas a valuable tool for increasing soil fertility, improving crop yields, and enhancing the resilience of agricultural production to unfavorable factors.
It is important to note that the agrochemical properties of biogas may vary depending on its composition, production processes, application methods, and the soil's own properties.
One advantage of biogas over high doses of mineral fertilizers is that it does not create excessive salt concentrations in the soil solution.This is due to its buffering properties.
Biogas has the ability to retain and regulate the availability of nutrients to plants.It acts as a kind of regulator of ion exchange in the soil, helping maintain a balance of salts in the soil solution.
Unlike high doses of mineral fertilizers, which can lead to the accumulation of excess ions in the soil, biogas provides a gradual release of nutrients over an extended period.This allows plants to more efficiently utilize available nutrients without the risk of excessive accumulation and associated problems.
The buffering properties of biogas also help maintain soil pH stability.It can help mitigate soil acidity or alkalinity, creating optimal conditions for plant growth and improving the efficient use of nutrients.

Conclusion
Studies show that the application of biogas can lead to an increase in the content of available phosphorus in the soil.Available phosphorus refers to the form of phosphorus that is accessible to plant roots and can be easily absorbed by them.
Furthermore, biogas can improve soil structure and promote the formation of aggregates, creating conditions for more efficient assimilation and utilization of phosphorus by plants.
The increase in available phosphorus content in the soil through the application of biogas can have a positive impact on the growth and development of plants, as phosphorus is one of the key nutrients required for DNA and RNA synthesis, enzyme production, and energy metabolism.It plays a vital role in energy exchange, root development, and flowering of plants.
Thus, the application of biogas to the soil can contribute to an increase in the content of available phosphorus, which can have a positive effect on the nutrient status of plants and overall soil productivity.The application of biogas obtained from vermicomposting, a process that involves the decomposition of organic materials by California red worms (Eisenia fetida), can increase the humus content in the soil and improve its fertility.
California red worms are effective decomposers of organic matter.They consume organic waste such as plant residues, manure, food scraps, etc., and convert them into stable and nutrient-rich compost.Through the processing of organic materials, the worms release excrements known as vermicompost or biogas.This biogas is rich in humus and has a high organic matter content.
The application of biogas to the soil leads to several positive effects: Increase in humus content: Biogas obtained from worms is a rich source of humus.Its application to the soil contributes to an increase in organic matter content, which positively affects soil structure, water retention capacity, and nutrient properties.
Improvement of soil structure: Vermicompost biogas helps enhance soil aggregation by forming stable granules and aggregates.This improves soil permeability to air, water, and plant roots.
Moisture retention: Biogas has a high water-holding capacity and the ability to retain moisture in the soil.It creates a reservoir of water that helps plants access moisture during drought periods and enhances plant resilience to stressful conditions.
Enhancement of biological activity: Biogas obtained from worms contains beneficial microorganisms that contribute to the activation of soil biological activity.This affects nutrient cycling, organic matter decomposition, and overall soil health improvement.
Therefore, the application of biogas obtained from California red worms contributes to an increase in humus content in the soil, leading to improved soil fertility and the ability to support healthy plant growth and development If the condition is me: