Results 171 to 180 of about 48,383 (208)

Factorization of operators I. Miura transformations

Journal of Mathematical Physics, 1980
The method of factorization of operators, which has been used to derive the Miura transformation of the KdV equation, is here extended to some third-order scattering operators, and transformations between several fifth-order nonlinear evolution equations are derived. Further applications are discussed.
Fordy, Allan P., Gibbons, John
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Miura Transformation for the TD Hierarchy

Chinese Physics Letters, 2006
Based on the spectral problem associated with the TD hierarchy, a recursion relation for the adjoined spectral problem is obtained, by which the TD hierarchy is transformed into the modified one. As a special example, the first nontrivial member in the modified hierarchy is reduced to an integrable Heisenberg spin equation.
Zhu Jun-Yi, Geng Xian-Guo
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On the polynomial Miura transformation

Physics Letters A, 1990
Abstract The polynomial Miura transformation ϕ = ω x + a ( ω ) ( a ( ω ) is an n th-power polynomial) connects continual classes of local evolution equations at n n ⩾3 it turns out to connect only the trivial equations ϕ t = ϕ x and ω t = ω x or some equivalent to them.
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Inversion of the Miura transformation

Mathematical Notes of the Academy of Sciences of the USSR, 1989
It is proved that the global (\(\forall\, x\in\mathbb{R})\) inverse Miura transformation is possible, more precisely, it is proved that the Riccati equation \(v(x,t)=u_x(x,t)+u^2(x,t)\) is solvable for all \(x\in\mathbb{R}\), under the boundary conditions \(u(x,t)\sim C_1\) (resp. \(C_2)\) for \(x\to -\infty\) (resp. \(x\to \infty)\), \(v(x,t)\sim a^2\)
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Miura transformation on a lattice

Theoretical and Mathematical Physics, 1988
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The Miura transformation, Bäcklund transformation and the problem of collision

Physics Letters A, 1976
Abstract The paper refutes the widespread opinion that collision of solitons with a non-soliton portion of a wave packet gives no asymptotic result. Based on the Generalized Miura Transformation (GMT), study is made of the problems of binary collisions for eqs. (1), (4), (11)-(14), (19)-(22) and a new form of the Backlund transformation for eqs. (4),
A.Kh. Fridman, M.M. El'yashevich
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Differential substitutions of the miura transformation type

Theoretical and Mathematical Physics, 1998
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Construction scheme for discrete Miura transformations

Journal of Physics A: Mathematical and General, 1994
Summary: A direct and elementary scheme for the construction of Miura-type transformations and discrete differential equations related to them (scalar and vector) is presented. The scheme is illustrated using as examples the Volterra and Toda models. A discrete differential analogue of the Calogero-Degasperis equation is discussed in detail.
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On Miura transformations of evolution equations

Journal of Physics A: Mathematical and General, 1993
Summary: The general Miura transformation \((t,x,u(t,x))\to(s,y,v(s,y))\): \(v=a(t,x,u,\dots,\partial^ ru/\partial x^ r)\), \(y=b(t,x,u,\dots,\partial^ ru/\partial x^ r)\), \(s=c(t,x,u,\dots,\partial^ ru/\partial x^ r)\) is considered which connects two evolution equations \(u_ t=f(t,x,u,\dots,\partial^ nu/\partial x^ n)\) and \(v_ s=g(t,x,u,\dots ...
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On Miura transformations among nonlinear partial differential equations

Journal of Mathematical Physics, 2006
In this paper, we study Miura transformations u↦v from partial differential equations uxxx=F(u,ux,ut) to nonlinear partial differential equations G(v,vx,vt,…,∂xlv,…,∂t1v)=0 defined using integrable systems on v. We classify all such Miura transformations under some restrictions, and hence generalize the classical Miura transformation to a large class ...
Cao, Xifang, Wu, Hongyou, Xu, Chuanyou
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