Remarks on the first integral method for solving nonlinear evolution equations
Aparna Saha, B. Talukdar Umapada Das, Supriya Chatterjee
TL;DR
The paper critiques the first integral method for solving nonlinear evolution equations, highlighting its limitations in providing only particular solutions for conservative systems and incorrect solutions for dissipative systems.
Contribution
It clarifies the applicability and limitations of the first integral method in solving nonlinear evolution equations, emphasizing its restricted validity.
Findings
The method yields only particular solutions for conservative systems.
It produces incorrect solutions for dissipative systems.
The critique guides better solution approaches for nonlinear evolution equations.
Abstract
We point out that use of the first integral method ( J.Phys. A :Math. Gen. 35 (2002) 343 ) for solving nonlinear evolution equations gives only particular solutions of equations that model conservative systems. On the other hand, for dissipative dynamical systems, the method leads to incorrect solutions of the equations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Black Holes and Theoretical Physics