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New exact solutions for the classical Drinfel’d-Sokolov-Wilson equation. (English) Zbl 1181.35221

Summary: We investigate the classical Drinfel’d-Sokolov-Wilson equation (DSWE)

u t +pvv t =0,v t +ruv x +su x v+qv xxx =0,

where p,q,r,s are some nonzero parameters. Some explicit expressions of solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain solitary wave solutions, blow-up solutions, periodic solutions, periodic blow-up solutions and kink-shaped solutions. Some previous results are extended.

MSC:
35Q51Soliton-like equations
35C08Soliton solutions of PDE
35B10Periodic solutions of PDE
35B44Blow-up (PDE)
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K50Bifurcation problems (infinite-dimensional systems)
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