Related papers: A synthetical two-component model with peakon solu…
A general form of $N$-dark soliton solutions of the multi-component Mel'nikov system is presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general…
The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink…
New classical integrable systems of Camassa-Holm peakon type are proposed. They realize the maximal even piecewise-D_2 generalization of the Calogero-Francoise flows, yielding periodic and pseudoperiodic trigonometric/hyperbolic potentials.…
We consider multipeakon solutions, and to some extent also multishockpeakon solutions, of a coupled two-component integrable PDE found by Geng and Xue as a generalization of Novikov's cubically nonlinear Camassa-Holm type equation. In order…
Using older and recent results on the integrability of two-dimensional (2d) dynamical systems, we prove that the results obtained in a recent publication concerning the 2d generalized Ermakov system can be obtained as special cases of a…
Port-Hamiltonian (pH) systems offer a highly structured and energy-based modular framework for control systems. Many pH systems exhibit non-polynomial non-linearities. We consider the problem of immersing such systems into a…
We study periodic solutions for a quasi-linear system, which is the so called dispersionless Lax reduction of the Benney moments chain. This question naturally arises in search of integrable Hamiltonian systems of the form $ H=p^2/2+u(q,t)…
This paper presents a novel framework for enclosing solutions of Poisson's equation based on generalized sub- and super-solutions constructed using fundamental solutions. The conventional definition of sub- and super-solutions based on…
In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato's theorem. Then we give the necessary and sufficient…
A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov equations that describe breaking waves is introduced. A classification of low-order conservation laws, peaked travelling wave solutions, and Lie…
We introduce a new mixed discontinuous/continuous Galerkin finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1dg-P2, uses discontinuous piecewise…
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
A system of two operator equations is considered - one of pseudomonotone type and the other of strongly monotone type - both being strongly coupled. Conditions are given that allow to reduce the solvability of this system to a single…
We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although…
In this paper, we study traveling wave solutions and peakon weak solutions of the modified Camassa-Holm (mCH) equation with dispersive term $2ku_x$ for $k\in\mathbb{R}$. We study traveling wave solutions through a Hamiltonian system…
In this paper, a new framework for studying the existence of generalized or strongly generalized solutions to a wide class of inclusion systems involving double-phase, possibly competing differential operators, convection, and mixed…
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023] to port-Hamiltonian systems describing linear wave propagation…
In this paper, we study the persistence properties and unique continuation for a dispersionless two-component system with peakon and weak kink solutions. These properties guarantee strong solutions of the two-component system decay at…
We obtain the bi-Hamiltonian structure for some of the two-component short pulse equations proposed in the literature to generalize the original short pulse equation when polarized pulses propagate in anisotropic media.
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…