On existence of kink and antikink wave solutions of singularly perturbed Gardner equation
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6204
Abstract: In this paper, we study the existence of kink and antikink wave solutions of singularly perturbed Gardner equation from the geometric perspective. We obtain the sufficient conditions to guarantee the existence of kink and antikink… read more here.
Keywords: solutions singularly; wave solutions; antikink wave; existence kink ... See more keywords
Asymptotic step-like solutions of the singularly perturbed Burgers equation
Sign Up to like & getrecommendations! Published in 2023 at "Physics of Fluids"
DOI: 10.1063/5.0150685
Abstract: This paper deals with a problem of asymptotic step-like solutions of the Burgers equation with variable coefficients and a small parameter. By means of the nonlinear Wentzel–Kramers–Brillouin method, the algorithm of constructing these asymptotic solutions… read more here.
Keywords: like solutions; step like; solutions singularly; burgers equation ... See more keywords
Gevrey Asymptotics for Logarithmic-Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities
Sign Up to like & getrecommendations! Published in 2023 at "Abstract and Applied Analysis"
DOI: 10.1155/2023/3025513
Abstract: We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter ϵ and singular in a complex time variable t at the origin. These equations combine differential operators of… read more here.
Keywords: singularly perturbed; gevrey asymptotics; logarithmic type; type solutions ... See more keywords
Heteroclinic solutions in singularly perturbed discontinuous differential equations: a non-generic case
Sign Up to like & getrecommendations! Published in 2024 at "Electronic Journal of Qualitative Theory of Differential Equations"
DOI: 10.14232/ejqtde.2024.1.27
Abstract: We derive Melnikov type conditions for the persistence of heteroclinic solutions in perturbed slowly varying discontinuous differential equations. Opposite to [J. Differential Equations 400(2024), 314–375] we assume that the unperturbed (frozen) equation has a parametric… read more here.
Keywords: singularly perturbed; differential equations; discontinuous differential; heteroclinic solutions ... See more keywords
Boundary layer solutions to singularly perturbed quasilinear systems
Sign Up to like & getrecommendations! Published in 2021 at "Discrete and Continuous Dynamical Systems - Series B"
DOI: 10.3934/dcdsb.2021226
Abstract: We consider weak boundary layer solutions to the singularly perturbed ODE systems of the type \begin{document}$ \varepsilon^2\left(A(x, u(x), \varepsilon)u'(x)\right)' = f(x, u(x), \varepsilon) $\end{document}. The new features are that we do not consider one scalar… read more here.
Keywords: singularly perturbed; case; solutions singularly; quasilinear systems ... See more keywords