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
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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
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
An optimized compact reconstruction weighted essentially non-oscillatory scheme for Degasperis-Procesi equation
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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