研究目的
The problem or phenomenon addressed in this study is the construction of solitons, elliptic function, and other solutions of the dimensionless time-dependent paraxial wave model in Kerr media using three mathematical techniques to understand the physical phenomena of this wave model.
研究成果
The study effectively constructed solitons and other solutions of the paraxial wave model in Kerr media using three mathematical techniques. These solutions have vital applications in engineering, optical fibers, and mathematical physics. The power and effectiveness of the current methods were verified from the obtained results and computational work, which can be used in other nonlinear models.
研究不足
The paper does not explicitly mention the technical and application constraints of the experiments or potential areas for optimization.
1：Experimental Design and Method Selection:
The study employs three mathematical techniques (improved simple equation technique, exp(?Φ(ζ))-expansion technique, and modified extended direct algebraic technique) to construct solutions of the paraxial wave model.
2：Sample Selection and Data Sources:
The study uses the dimensionless time-dependent paraxial wave model in Kerr media as the basis for constructing solutions.
3：List of Experimental Equipment and Materials:
Not explicitly mentioned in the paper.
4：Experimental Procedures and Operational Workflow:
The paper describes the application of the three mathematical techniques to the paraxial wave model, including the derivation of solutions and the graphical depiction of soliton structures.
5：Data Analysis Methods:
The paper discusses the physical interpretation of the obtained solutions and their applications in engineering, optical fibers, and mathematical physics.
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