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Solving the one-loop soliton solution of the Vakhnenko equation by means of the homotopy analysis method. (English) Zbl 1069.35060
Summary: A powerful, easy-to-use analytic technique for nonlinear problems, namely the homotopy analysis method, is applied to solve the Vakhnenko equation, a nonlinear equation with loop soliton solutions governing the propagation of high-frequency waves in a relaxing medium. By means of a transformation of independent variables, an analysis of one-loop soliton solution expressed by a series of exponential functions is obtained, which agrees well with the known exact solution.

MSC:
35Q35 PDEs in connection with fluid mechanics
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
76A10 Viscoelastic fluids
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