Analytic and loop solutions for the K(2,2) equation (focusing branch)
نویسندگان
چکیده
In this paper, we study analytic and loop solutions of the K(2,2) equation(focusing branch), which is first proposed by Rosenau. The implicit analytic and loop solutions are obtained by using the dynamical system approach. Moreover, we investigate how the famous Rosenau-Hyman compactons can be recovered as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical system by theoretical analysis and numerical simulation. c ©2016 All rights reserved.
منابع مشابه
Nonlinear Fuzzy Volterra Integro-differential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution
This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...
متن کاملTHE REVIEW OF ALMOST PERIODIC SOLUTIONS TO A STOCHASTIC DIERENTIAL EQUATION
This paper proves the existence and uniqueness of quadratic mean almost periodic mild so-lutions for a class of stochastic dierential equations in a real separable Hilbert space. Themain technique is based upon an appropriate composition theorem combined with the Banachcontraction mapping principle and an analytic semigroup of linear operators.
متن کاملGeneral Solution for Fuzzy Linear Second Order Differential Equation Using First Solution
The fuzzy linear second order equations with fuzzy initial values are investigatedin this paper. The analytic general solution solutions of them usinga rst solution is founded. The parametric form of fuzzy numbers is appliedto solve the second order equations. General solutions for fuzzy linear secondorder equations with fuzzy initial values are investigated and formulatedin four cases. A examp...
متن کاملModeling of Refractive Indices for Binary Aqueous Solutions of Some Alkane Polyols at Constant Temperature and Pressure
In this research, a theoretical study has been undertaken on the density and also on the relationship between refractive index and density for aqueous solutions. A simple linear equation is suggested to show this relationship. Also, a semi-empirical equation has been developed for estimating the constant of this linear equation. By using our suggested equations, the refractive indices of aq...
متن کاملConvergence of Solitary - Wave Solutions in Aperturbed Bi - Hamiltonian Dynamical System
In this part, we prove that the solitary wave solutions investigated in part I are extended as analytic functions in the complex plane, except at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex sin-gularities allows the creation of non-analytic solutions with corners and/or compact support. This is the second in a series of two ...
متن کامل