Exact solitary and periodic-wave solutions of the \(K(2,2)\) equation (defocusing branch). (English) Zbl 1202.35185

Summary: An auxiliary elliptic equation method is presented for constructing exact solitary and periodic travelling-wave solutions of the \(K(2,2)\) equation (defocusing branch). Some known results in the literature are recovered more efficiently, and some new exact travelling-wave solutions are obtained. Also, new stationary-wave solutions are obtained.


35Q51 Soliton equations
35C07 Traveling wave solutions
35C08 Soliton solutions
35B10 Periodic solutions to PDEs
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