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General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive $$K(n,n)$$ equations in higher dimensional spaces. (English) Zbl 1027.35118
Summary: The defocusing branch of the genuinely nonlinear dispersive $$K(n,n)$$ equation that exhibits solutions with solitary patterns is investigated. The equation, with constant coefficients to the derivatives, is examined in one-, two- and three-dimensional spaces. General formulas for solutions with solitary patterns are developed for all positive integers $$n$$, $$n>1$$.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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