Compactons and Riemann Waves of an Extended Modified Korteweg–de Vries Equation with Nonlinear Dispersion
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The K(f m , g n ) equation is studied, which generalizes the modified Korteweg–de Vries equation K(u3, u1) and the Rosenau–Hyman equation K(u m , u n ) to other dependences of nonlinearity and dispersion on the solution. The considered functions f(u) and g(u) can be linear or can have the form of a smoothed step. It is found numerically that, depending on the form of nonlinearity and dispersion, the given equation has compacton and kovaton solutions, Riemann-wave solutions, and oscillating wave packets of two types. It is shown that the interaction between solutions of all found types occurs with the preservation of their parameters.
KeywordsKdV equation mKdV equation K(m, n) equation Rosenau–Hyman equation K(cos) equation the Rosenau–Pikovsky equation compacton kovaton soliton kink Riemann wave oscillatory waves wave packets multisoliton interaction
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