Related papers: The modified Camassa-Holm equation in Lagrangian c…
In this paper, we prove the global existence of H\"older continuous solutions for the Cauchy problem of a family of partial differential equations, named as $\lambda$-family equations, where $\lambda$ is the power of nonlinear wave speed.…
We introduce a large class of modifications of the standard lagrangian for two dimensional dilaton gravity, whose general solutions are nonsingular black holes. A subclass of these lagrangians have extremal solutions which are nonsingular…
In this paper, we show the global existence and uniqueness of classical solutions of the Maxwell-Chern-Simmons-Higgs system coupled to a neutral scalar with nontrivial scalar potential on (2+1) dimensional Minkowski spacetime. Our methods…
This paper investigates the Cauchy problem of a generalized Camassa-Holm equation with quadratic and cubic nonlinearities (alias the mCH-Novikov-CH equation), which is a generalization of some special equations such as the Camassa-Holm (CH)…
The present paper is mainly concerned with the blow-up phenomena and exponential decay of solution for a three-component Camassa-Holm equation. Comparing with the result of Hu, ect. in the paper[1], a new wave-breaking solution is obtained.…
Multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds, given by Lagrangians or Hamiltonians which have quadratic growth in the velocities or in the momenta.…
In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the…
The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous background magnetic field. First, the MHD system is…
The Camassa-Holm equation (CH) is a well known integrable equation describing the velocity dynamics of shallow water waves. This equation exhibits spontaneous emergence of singular solutions (peakons) from smooth initial conditions. The CH…
In this paper, we will study the existence of finite time singularity to harmonic heat flow and their formation patterns. After works of Coron-Ghidaglia, Ding and Chen-Ding, one knows blow-up solutions under smallness of initial energy for…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
In this paper, we consider the 3-D compressible isentropic MHD equations with infinity electric conductivity. The existence of unique local classical solutions is firstly established when the initial data is arbitrarily large, contains…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
We analyse the one-dimensional pressureless Euler-Poisson equations with a linear damping and non-local interaction forces. These equations are relevant for modelling collective behavior in mathematical biology. We provide a sharp threshold…
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…
In this paper, we study orbital stability of peakons for the generalized modified Camassa-Holm (gmCH) equation, which is a natural higher-order generalization of the modified Camassa-Holm (mCH) equation, and admits Hamiltonian form and…
It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also decays exponentially at a later time. In particular, a…
We consider the physical model of a classical mechanical system (called "small system") undergoing repeated interactions with a chain of identical small pieces (called "environment"). This physical setup constitutes an advantageous way of…