dear friends
I am attempting to construct lax pair for nonlinear evolution equations. As a beginner, working on already solved lax pair equations such as nonlinear schrodinger equation, kdv and sine gordon using the AKNS method. Is it possible to construct lax pair for equations which are derived using perturbation techniques? say for example, landau-Lifshitz equation for spin evolution of ferromagnets is reduced to a scalar nonlinear equation through reductive perturbation. Is it possible to construct the lax pair for this equation. See the attachment.
Hello! the first question one may ask is whether your equation does admit a Lax pair ?
Having this type of property implies that the PDE is solvable by means of the inverse scattering method, quite a strong requirement (exact solvability). It has to be integrable too. Wikipedia gives you a preliminary list of eqns admitting Lax pairs:
https://en.wikipedia.org/wiki/Lax_pair
I am a bit confused. First of all, what is h in your equation? Is it an arbitrary function of z or some thing different? Can you give a reference to a paper where your equation is derived?
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