相关论文: Exact quasi-periodic solutions to the sine(sinh)-G…

The generalized sine-Gordon (sG) equation $u_{tx}=(1+\nu\partial_x^2)\sin\,u$ was derived as an integrable generalization of the sG equation. In a previous paper (Matsuno Y 2010 J. Phys. A: Math. Theor. {\bf 43} 105204) which is referred to…

The numerical approximation of the semilinear Klein--Gordon equation in the $d$-dimensional space, with $d=1,2,3$, is studied by analyzing the consistency errors in approximating the solution. By discovering and utilizing a new cancellation…

Close to the origin, the nonlinear Klein--Gordon equations on the circle are nearly integrable Hamiltonian systems which have infinitely many almost conserved quantities called harmonic actions or super-actions. We prove that, at low…

We have studied the solutions of the combined sine-cosine-Gordon Equation found by Wazwaz (App. Math. Comp. 177, 755 (2006)) using the variable separated ODE method. These solutions can be transformed into a new form. We have derived the…

We present a set of time quasi-periodic solutions to a nonlinear Klein-Gordon equation with a decaying nonlinear term on the torus in arbitrary dimensions. This paper generalizes the bifurcation method developed in [W2].

The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, non-integrable systems belonging to the sine-Gordon family at finite…

The generalized Sinh-Gordon potential is solved within quantum Hamiltonian Jacobi approach in the framework of PT symmetry. The quasi exact solutions of energy eigenvalues and eigenfunctions of the generalized Sinh-Gordon potential are…

Employing the Hirota's method, a class of soliton solutions for the N=2 super mKdV equations is proposed in terms of a single Grassmann parameter. Such solutions are shown to satisfy two copies of N=1 supersymmetric mKdV equations connected…

The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line $x\leq 0$ with local boundary condition at the origin is considered. The most…

We give arguments for the existence of {\it exact} travelling-wave (in particular solitonic) solutions of a perturbed sine-Gordon equation on the real line or on the circle, and classify them. The perturbation of the equation consists of a…

We study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also…

A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…

The semi-classical spectrum of the Homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive…

This paper concerns the existence of multiple rotating quasi-periodic solutions for second order Hamiltonian systems with sub-quadratic potential. Such solutions have the form $x(t+T)=Qx(t)$ for some orthogonal matrix $Q$. To deal with such…

In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation $u_{t x}=\left(1+\nu \partial_x^2\right) \sin u$. The bilinear equations of the discrete KP hierarchy and the proper definition of discrete…

This is a short review of the construction of quasi-periodic (algebraic-geometrical) solutions to hierarchies of nonlinear integrable equations. As is well known, the solutions are expressed through Riemann's theta-functions associated with…

We perform some simulations of the semilinear Klein--Gordon equation with a power-law nonlinear term and propose each of the quantitative evaluation methods for the stability and convergence of numerical solutions. We also investigate each…

We have constructed the quasi-exactly-solvable two-mode bosonic realizations of su(2) and su(1, 1) algebra. We derive the relations leading to the conditions for quasi-exact solvability of two-boson Hamiltonians by determining a general…

In this paper, an implicit time stepping meshless scheme is proposed to find the numerical solution of high-dimensional sine-Gordon equations (SGEs) by combining the high dimensional model representation (HDMR) and the Fourier hyperbolic…

We study the elliptic sinh-Gordon and sine-Gordon equations on the real plane and we introduce new families of solutions. We use a Backlund transformation that connects the elliptic versions of sinh-Gordon and sine-Gordon equations. As an…