Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
The problem of existence of solitary wave solutions to some higher-order model evolution equations arising from water wave theory is discussed. A simple direct method for finding monotone solitary wave solutions is introduced, and by exhibiting explicit necessary and sufficient conditions, it is illustrated that a model admit exact ${\text{sech}}^2 …