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An analysis of the Zhiber-Shabat equation including Lie point symmetries and conservation laws. (English) Zbl 1334.35290

Summary: We address the integrability aspects of the Zhiber-Shabat equation that serves as a generalised version of the \(\Phi -4\) equation which is related to relativistic quantum mechanics. Three methods of integration are applied to this nonlinear evolution equation, namely the travelling-wave approach, Lie group method and the invariance-multiplier approach.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35C07 Traveling wave solutions
33E05 Elliptic functions and integrals

Software:

GeM
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References:

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