Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
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DOI: 10.1007/s10884-016-9529-3
Abstract: In this paper, we consider the perturbed KdV equation with Fourier multiplier $$\begin{aligned} u_{t} =- u_{xxx} + \big (M_{\xi }u+u^3 \big )_{x},\quad u(t,x+2\pi )=u(t,x),\quad \int _0^{2\pi }u(t,x)dx=0, \end{aligned}$$ut=-uxxx+(Mξu+u3)x,u(t,x+2π)=u(t,x),∫02πu(t,x)dx=0,with analytic data of size $$\varepsilon $$ε. We… read more here.
Keywords: real analytic; periodic solutions; perturbed kdv; quasi periodic ... See more keywords
Obtaining new soliton solutions of the fractional generalized perturbed KdV equation
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DOI: 10.1088/1402-4896/ad8846
Abstract: In this study, the fractional generalized perturbed KdV equation (gpKdV) with beta derivative is considered. The generalized exponential rational function method (GERFM) is applied to this equation for the first time in this study. Thus,… read more here.
Keywords: equation; perturbed kdv; fractional generalized; function ... See more keywords