Asymptotic states in long Josephson junctions are investigated in an external magnetic field. We show that a choice one of the solution of the stationary Ferrell-Prange equation can carry be out with use of an asymptotic solution of the sine-Gordon equation and that an evolution to that stable solution occurs by passing through metastable states, which is determined with a form of quickly dampe...

In this article, we establish the existence and uniqueness of (c1)-differentiable (c2)- differentiable solutions to first-order nonlinear impulsive fuzzy differential equations under generalized Hukuhara differentiability using contraction mappings principle. particular, are written as hyperbolic cosine sine functions with terms, which is main difficulty. An example provided prove our results.

In this work we apply an extended hyperbolic function method to solve the nonlinear family of third order Korteweg de-Vries (KdV) equations, namely, the KdV equation, the modified KdV (mKdV) equation, the potential KdV (pKdV) equation, the generalized KdV (gKdV) equation and gKdV with two power nonlinearities equation. New exact travelling wave solutions are obtained for the KdV, mKdV and pKdV ...

Poly-Cauchy numbers with level 2 are defined by inverse sine hyperbolic functions the relation from functions. In this paper, we introduce Stirling of first kind in order to establish some relations poly- Cauchy 2. Then, show several convolution identities poly-Cauchy particular, that three can be expressed as a simple form.

This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation presence of a detuning factor. The φ^6-model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic well combined solutions model. results presented this study are intended improve CGLE's dynamical characteristics, i...

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gor...

This paper studies a perturbative approach for the double sine–Gordon equation. Following this path, we are able to obtain system of differential equations that shows amplitude and phase modulation approximate solution. In case λ = 0, get well-known perturbation theory For special value −1/8, derive phase-locked solution with same frequency linear case. general, both coherent (solitary waves, l...

In this paper, it is shown that D. Shelupsky’s generalized sine function, and various general sine functions developed by P. Drábek, R. Manásevich and M. Ôtani, P. Lindqvist, including the generalized Jacobi elliptic sine function of S. Takeuchi can be defined by systems of first order nonlinear ordinary differential equations with initial conditions. The structure of the system of differential...

Using a field theory generalization of the spinning top motion, we construct nonabelian generalizations of the sine-Gordon theory according to each symmetric spaces. A La-grangian formulation of these generalized sine-Gordon theories is given in terms of a deformed gauged Wess-Zumino-Witten action which also accounts for integrably perturbed coset conformal field theories. As for physical appli...