研究目的
To recover optical soliton solutions in (2+1)-dimensions for the Kundu–Mukherjee–Naskar equation using the extended trial function method.
研究成果
The paper successfully secured bright and singular optical soliton solutions to the Kundu–Mukherjee–Naskar equation using the extended trial function method. These solutions, including Jacobi's elliptic function-based ones, are reported for the first time. Future research should focus on stability analysis and applying other methods to find further solutions.
研究不足
The stability of the solutions has not been addressed in the paper. Future work will involve numerical algorithms to analyze stability and apply additional integration methodologies.
1：Experimental Design and Method Selection:
The extended trial function method was employed to solve the Kundu–Mukherjee–Naskar equation, which governs soliton dynamics in (2+1)-dimensions. This method involves assuming a specific form for the soliton amplitude and solving the resulting equations to derive exact solutions.
2：Sample Selection and Data Sources:
No specific samples or datasets were used, as the study is theoretical and mathematical, focusing on deriving analytical solutions.
3：List of Experimental Equipment and Materials:
No experimental equipment or materials were mentioned, as the work is purely mathematical.
4：Experimental Procedures and Operational Workflow:
The procedure included inserting a hypothesis for the soliton structure into the governing equation, decomposing into real and imaginary parts, and applying the extended trial function method to balance and solve the equations, leading to various solution forms.
5：Data Analysis Methods:
Analytical methods were used to derive and classify solutions, including taking limiting values of parameters to obtain specific soliton types.
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