Abstract We derive a modulation theory for the resolution of radially symmetric kink waves governed by multi-dimensional sine-Gordon equation. Whitham is developed to explain return an expanding wave, as well predicting its maximum expansion radius and time. Comparisons with full numerical solutions equation show that gives excellent predictions not only returning time radius, but also details ...

In this paper, we investigate local and nonlocal reductions of a discrete negative order Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, construct exact solutions in double Casoratian form to reduced sine-Gordon equations. Then, semidiscrete equations their are obtained through continuum limits. The dynamics soliton analyzed illustrated by asymptotic analysis. rese...

In this paper, a type of fully nonlinear Sine-Gordon equations and the approximate Sine-Gordon equation (under the condition: |up|is very small) are studied.Through proper transformation, some initial value problems of many equations with special nonlinear terms are solved by the Adomian decomposition method and some exact solutions: kink solution ,compacton solution, multi-compacton solution, ...

In this paper, we give a sufficient conditions for the exact controllability of the non-linear generalized damped wave equation ẅ + ηẇ + γAw = u(t) + f(t, w, u(t)), on a Hilbert space. The distributed control u ∈ L2 and the operator A is positive definite self-adjoint unbounded with compact resolvent. The nonlinear term f is a continuous function on t and globally Lipschitz in the other variabl...

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution employing the thin plate splines (TPS) radial basis function (RBF). The new scheme works in a similar fashi...

Abstract: In this paper, differential transform method (DTM) is applied to the sine-Gordon equation which arise in differential geometry, propagation of magnetic flux, stability of fluid motions, nonlinear physics and applied sciences. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational task. Exact solutions can also be ac...

Algebro-geometric Poisson brackets for real, finite-zone solutions of the Korteweg–de Vries (KdV) equation were studied in [1]. The transfer of this theory to the Toda lattice and the sinh-Gordon equation is more or less obvious. The complex part of the finite-zone theory for the nonlinear Schrödinger equation (NS) and the sine-Gordon equation (SG) is analogous to KdV, but conditions that solut...