Solitary wave solutions for a generalized KdV–mKdV equation with distributed delays

<abstract><p>This paper investigates a delayed shallow water fluid model that has not been studied in previous literature. Applying geometric singular perturbation theory, we prove the existence of traveling wave solutions for the model with a nonlocal weak delay kernel and local strong delay convolution kernel, respectively. When the convection term contains a nonlocal weak generic delay kernel, the desired heteroclinic orbit is obtained by using Fredholm theory and linear chain trick to prove the existence of two kink wave solutions under certain parametric conditions. When the model contains local strong delay convolution kernel and weak backward diffusion, under the same parametric conditions to the previous case, the corresponding traveling wave system can be reduced to a near-Hamiltonian system. The existence of a unique periodic wave solution is established by proving the uniqueness of zero of the Melnikov function. Uniqueness is proved by utilizing the monotonicity of the ratio of two Abelian integrals.</p></abstract>

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Solitary wave solutions for a generalized KdV–mKdV equation with distributed delays

Cited by 3 publications

References 23 publications

Solitary waves solutions of singularly perturbed higher-order KdV equation via geometric singular perturbation method

Solitary waves solutions of singularly perturbed higher-order KdV equation via geometric singular perturbation method

New solitary and optical wave structures to the (1 + 1)-dimensional combined KdV–mKdV equation

Existence of traveling waves in a delayed convecting shallow water fluid model

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