Title

Coherent Structures Of The Φ4 Equation Via Invariant Painlevé Analysis

Keywords

Accessibility from Initial Conditions; Analysis; Coherent Structures; Painlevé

Abstract

Exact closed-form coherent structures (pulses/fronts/domain walls) having the form of complicated traveling waves are constructed via invariant Painlevé analysis for the Φ4 equation, which belongs to the family of Klein-Gordon equations. These analytical solutions, which are derived directly from the underlying PDE's. are investigated in the light of restrictions imposed by the ODE that any traveling wave reduction of corresponding PDE must satisfy. In particular, it is shown that the coherent structures a) asymptoticaly satisfy the ODE governing traveling wave reductions, and b) are accessible to the PDE from compact support initial conditions. The solutions are compared with each other, and with previously known solutions of the equation.

Publication Date

4-1-2002

Publication Title

Indian Journal of Pure and Applied Mathematics

Volume

33

Issue

4

Number of Pages

495-508

Document Type

Article

Personal Identifier

scopus

Socpus ID

0036555697 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0036555697

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