On the Korteweg-de Vries equation: an associated equation.

Schlereth, Eugene P.; Rodin, Ervin Y.

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Higher-order equations of the KdV type are integrable.

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Variable depth KdV equations and generalizations to more nonlinear regimes

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We study here the water waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known that, for such regimes, a generalization of the KdV equation (somehow linked to the Camassa-Holm equation) can be derived and justified [Constantin and Lannes, (2009) 165–186] when the bottom is flat. We generalize here this result with a new class of equations taking into account variable bottom...

Wave fronts to some modifications of Korteweg-de Vries and Burgers-Korteweg-de Vries equations

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The existence of a traveling wave with special properties to modified KdV and BKdV equations is proved. Nonlinear terms in the equations are defined by means of a function f of an unknown u satisfying some conditions.