Soliton and periodic wave solutions to the osmosis equation.
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Mathematical Problems in Engineering
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Soliton and periodic wave solutions to the osmosis equation.
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Anti-periodic traveling wave solutions to a class of higher-order Kadomtsev-Petviashvili-Burgers equations.
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Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation.
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Existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced, nonlinear wave equations with periodic spatial boundary conditions is established. We consider both the cases the forcing frequency is (Case A) a rational number and (Case B) an irrational number.
Doubly periodic traveling waves in a cellular neural network with linear reaction.
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Nonlinear vibrations of completely resonant wave equations
Massimiliano Berti (2007)
Banach Center Publications
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We present recent existence results of small amplitude periodic and quasi-periodic solutions of completely resonant nonlinear wave equations. Both infinite-dimensional bifurcation phenomena and small divisors difficulties occur. The proofs rely on bifurcation theory, Nash-Moser implicit function theorems, dynamical systems techniques and variational methods.