Remarks on the first integral method for solving nonlinear evolution equations

2015/04/08 by Aparna Saha, Saha, Aparna, B. Talukdar Umapada Das +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #nlin.SI

paper · pdf · doi:10.48550/arxiv.1504.01890

openalex publication_date 2015/04/08 · arxiv created 2015/05/03 · arxiv updated 2015/05/05 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28

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.

Related

• Overcoming Obstacles to Integrability in Perturbed Nonlinear Evolution Equations
• Variational resolution for some general classes of nonlinear evolutions. Part II
• Integrability Tests for Nonlinear Evolution Equations
• Existence of solution to an evolution equation and a justification of the DSM for equations with monotone operators
• The Dynamical Systems Method for solving nonlinear equations with monotone operators