## Exact special solitary solutions with compact support for the nonlinear dispersive $$K$$($$m$$, $$n$$) equations.(English)Zbl 1088.35547

Summary: The nonlinear dispersive $$K(m,n)$$ equations, $u_{t}-(u^{m})_{x}-(u^{n})_{xxx} = 0$ which exhibit compactons: solitons with compact support, are studied. New exact solitary solutions with compact support are found. The two special cases, $$K$$(2, 2) and $$K$$(3, 3), are chosen to illustrate the concrete features of the decomposition method in $$K(m, n)$$ equations. General formulas for the solutions of $$K(m, n)$$ equations are established.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35C05 Solutions to PDEs in closed form

### Keywords:

solitons with compact support; decomposition method
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### References:

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