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Bifurcation approach to analysis of travelling waves in nonlocal hydrodynamic-type models. (English) Zbl 1474.35541

Summary: The paper considers the nonlocal hydrodynamic-type systems which are two-dimensional travelling wave systems with a five-parameter group. We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behavior of the travelling wave solutions. The existence of peakons, compactons, and periodic cusp wave solutions is discussed. When the parameter \(n\) equals 2, namely, let the isochoric Gruneisen coefficient equal 1, some exact analytical solutions such as smooth bright solitary wave solution, smooth and nonsmooth dark solitary wave solution, and periodic wave solutions, as well as uncountably infinitely many breaking wave solutions, are obtained.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B10 Periodic solutions to PDEs
35C07 Traveling wave solutions
35C08 Soliton solutions
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