Solvability of the Stochastic Degasperis-Procesi Equation
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DOI: 10.1007/s10884-021-10021-5
Abstract: This article studies the Stochastic Degasperis-Procesi equation on $$ \mathbb {R}$$ with an additive noise. Applying the kinetic theory, and considering the initial conditions in $$L^2(\mathbb {R})\cap L^{2+\delta }( \mathbb {R})$$ , for arbitrary small… read more here.
Keywords: stochastic degasperis; procesi equation; degasperis procesi; solvability ... See more keywords
Adaptive moving knots meshless method for Degasperis-Procesi equation with conservation laws
Sign Up to like & getrecommendations! Published in 2019 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2019.02.007
Abstract: Abstract The nonlinear Degasperis-Procesi (DP) equation allows shock wave solutions and possesses bi-Hamiltonian properties. Considering both of the two properties, we introduce a numerical scheme which involves three key features. First, a stable moving knots… read more here.
Keywords: procesi equation; knots meshless; moving knots; conservation laws ... See more keywords
Changes in the physical structures for new versions of the Degasperis-Procesi-Camassa-Holm model
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DOI: 10.1016/j.cjph.2020.11.010
Abstract: Abstract The goal of this work is to develop new solutions for modified versions of Degasperis-Procesi and Camassa-Holm model (DP-CH). In earlier studies, it has been observed that the new modification caused a deformation in… read more here.
Keywords: holm model; camassa holm; procesi camassa; model ... See more keywords
On the integrability of Degasperis–Procesi equation: Control of the Sobolev norms and Birkhoff resonances
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DOI: 10.1016/j.jde.2018.09.003
Abstract: We consider the dispersive Degasperis-Procesi equation $u_t-u_{x x t}-\mathtt{c} u_{xxx}+4 \mathtt{c} u_x-u u_{xxx}-3 u_x u_{xx}+4 u u_x=0$ with $\mathtt{c}\neq 0$. In \cite{Deg} the authors proved that this equation possesses infinitely many conserved quantities. We prove… read more here.
Keywords: procesi equation; control sobolev; sobolev norms; degasperis procesi ... See more keywords
On the finite time singularities for a class of Degasperis–Procesi equations
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Analysis: Real World Applications"
DOI: 10.1016/j.nonrwa.2018.04.005
Abstract: Abstract As we all know, the conservation laws take an important part in deriving wave breaking for Degasperis–Procesi (DP) type equation. In the article, we give a new method to study singularities in finite time… read more here.
Keywords: class; degasperis procesi; finite time; time singularities ... See more keywords
An optimized compact reconstruction weighted essentially non-oscillatory scheme for Degasperis-Procesi equation
Sign Up to like & getrecommendations! Published in 2020 at "Numerical Heat Transfer, Part B: Fundamentals"
DOI: 10.1080/10407790.2020.1713651
Abstract: Abstract This article presents a two-step iterative method that uses u – P formulation to study a Degasperis-Procesi (DP) equation, with which the DP equation is decomposed into the nonlinear advection equation and the Helmholtz… read more here.
Keywords: degasperis procesi; procesi equation; scheme; compact reconstruction ... See more keywords
Breaking and permanent waves for the periodic μ-Degasperis–Procesi equation with linear dispersion
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DOI: 10.1186/s13662-018-1873-7
Abstract: Considered herein is the periodic μ-Degasperis–Procesi equation, which is an evolution equation on the space of tensor densities over the Lie algebra of smooth vector fields. First two conditions on the initial data that lead… read more here.
Keywords: degasperis procesi; evolution; procesi equation; permanent waves ... See more keywords
A Computational Scheme for the Numerical Results of Time-Fractional Degasperis-Procesi and Camassa-Holm Models
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DOI: 10.3390/sym14122532
Abstract: This article presents an idea of a new approach for the solitary wave solution of the modified Degasperis–Procesi (mDP) and modified Camassa–Holm (mCH) models with a time-fractional derivative. We combine Laplace transform (LT) and homotopy… read more here.
Keywords: camassa holm; degasperis procesi; time fractional;
Numerical Analysis of Fractional-Order Camassa-Holm and Degasperis-Procesi Models
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DOI: 10.3390/sym15020269
Abstract: This study proposes innovative methods for the time-fractional modified Degasperis–Procesi (mDP) and Camassa–Holm (mCH) models of solitary wave solutions. To formulate the concepts of the homotopy perturbation transform method (HPTM) and Elzaki transform decomposition method… read more here.
Keywords: camassa holm; degasperis procesi; method;