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Non-integrable KdV-like models: solitons, breathers, compactons and rogue waves

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HY2W01 - Modulation theory and dispersive shock waves

We analyze the solutions of the KdV-like equation $ u_t [F (u)]_x u_xxx = 0 $, where the leading term is $ F (u) ∼ um $ or $ u|q $, with the rationales m and q. The well-known integrable KdV equations with m = 2 or 3 are particular cases of the generalized equation. We found analytically travelling waves in the form of solitons with exponential tails, algebraic solitons and compactons for various values of the exponents in the nonlinear term. Numerical simulations demonstrate the travelling wave stability and the weak inelasticity at the wave collisions. Breathers and rogue waves appeared numerically in the random wave field described by this equation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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