2 edition of **Prolongation structures and nonlinear evolution equations in two spatial dimensions** found in the catalog.

Prolongation structures and nonlinear evolution equations in two spatial dimensions

Hedley Clive Morris

- 40 Want to read
- 28 Currently reading

Published
**1976** by Trinity College. School of Mathematics in Dublin .

Written in English

**Edition Notes**

Statement | (by) H.C. Morris. 2, a generalized nonlinear Schrodinger equation. |

Contributions | Dublin University. School of Mathematics. |

The Physical Object | |
---|---|

Pagination | 14 leaves |

Number of Pages | 14 |

ID Numbers | |

Open Library | OL19268212M |

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The prolongation structure approach of Wahlquist and Estabrook is used to determine an inverse scattering formulation for a generalization of the nonlinear SchrĂ¶dinger equation to two spatial by: Â The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear SchrĂ¶dinger equation.

The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is openâi.e., does not terminate as a set of structure relations of a finiteâdimensional Cited by: Â The equations of nonlinear waveâenvelope interactions and the KadomtsevâPetviashvilliâDryuma equation are considered in detail.

The prolongation structure approach of Wahlquist and Estabrook is used to determine nonlinear evolution equations in two spatial dimensions for which an inverse scattering formulation by: The prolongation structure approach of Wahlquist and Estabrook is used to determine an inverse scattering formulation for a generalization of the nonlinear SchrĂ¶dinger equation to two spatial dimensions.

Bibtex entry for this abstract Preferred format for this abstract (see Preferences). The prolongation structure approach of Wahlquist and Estabrook is used to determine nonlinear evolution equations in two spatial dimensions for which an inverse scattering formulation exists.

The equations of nonlinear wave-envelope interactions and the Kadomtsev-Petviashvilli-Dryuma equation are considered in detail. Morris, H.C. Prolongation structures and nonlinear evolution equations in two spatial dimensions. A generalized nonlinear SchrĂ¶dinger equation.

Math. Phys. 18, â [Google Scholar] Karsten, T. Hamiltonian form of the modified nonlinear SchrĂ¶dinger equation for gravity waves on arbitrary depth.

by: 4. Field Equation Einstein Equation Killing Vector Nonlinear Evolution Equation Riemann Tensor These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm by: 2. See for example H.C. Morris, âProlongation Structure and Nonlinear Evolution Equations in Two Spatial Dimensions,â J.

Math. Phys. 17, (), and âInverse Scattering Problems in Higher Dimensions: Yang-Mills Fields and the Supersymmetric Sine-Gordon Equation,â J. by: 8. where Ï is a complex function. Recently Morrisâs prolongation structure theory for nonlinear evolution equation in two spatial dimensions [8] has been successfully applied to analyze equation (3) in Ref.[9].

It is noted that this prolongation structure method is very simple and eïŹective in the investigation of M-I equation. form of the equation is simpli ed, the size of the state space is increased, and the special structure of the evolution equation is obscured.

Nevertheless, when considering evolution equations in an abstract sense, we may restrict our attention to equations of the form ().

There are many questions which can be asked about evolution equa-File Size: KB. The prolongation structure approach of Wahlquist and Estabrook is used to determine nonlinear evolution equations in two spatial dimensions for which an. Differential Form Killing Vector Exterior Derivative Star Operator Prolongation Procedure These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm by: 1. We extend the fermionic covariant prolongation structure technique to the multidimensional super nonlinear evolution equation and present the fermionic covariant fundamental equations determining.

Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on OctoberThis book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational.

Morris, Prolongation structures and nonlinear evolution equations in two spatial dimensions. A generalized nonlinear SchrĂ¶dinger equation.

Math. Phys. 18. Reducing a generalized DaveyâStewartson system to a non-local nonlinear SchrĂ¶dinger equation. H.C. MorrisProlongation structures and nonlinear evolution equations in two spatial dimensions. J Math Phys, 17 (), pp. Cited by: 5.

In summary, we have investigated the prolongation structures of a generalized coupled KdV equation. As a result, two integrable coupled KdV equations associated with Lax pairs are obtained.

One is the general case of Qinâs equation and the other general case Wuâs equation [8].Cited by: The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions.

Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete prolongation Lie algebra, a whole family of nonlinear field equations containing the original Heisenberg system Cited by: 5.

In this paper the concept of pseudopotential is generalized to non-linear evolution equations in 2 + 1 dimensions. If the equations satisfied by the pseudopotential are of a Riccati-type in the x-variable, it is shown how to obtain both the generalized AKNS system and the auto-BĂ€cklund transformation for the corresponding non-linear evolution by: 5.

The prolongation structure approach of Wahlquist and Estabrook is used to determine nonlinear evolution equations in two spatial dimensions for which an inverse scattering formulation exists.

The. The KadomtsevâPetviashvili (KP) equation [10] is a nonlinear partial differential equation in two spatial and one temporal coordinate, which describes the evolution of nonlinear, long waves of small amplitude with slow dependence on the transverse coordinate.

A non-Abelian prolongation algebra for the three-wave resonant equations in one time and two spatial dimensions is derived. A SL3,c quotient algebra is used to find the linear eigenvalue problem associated with the equations under by: The prolongation structure approach of Wahlquist and Estabrook is used to determine an inverse scattering formulation for a generalization of the nonlinear SchrĂ¶dinger equation to two spatial.

2 +1 (i.e., two spatial dimensions and one time dimension). In addition, soli-ton solutions have been found in semi-discrete (discrete in space, continuous in time) and doubly discrete (discrete in space and time) nonlinear evolution equations and in nonlinear singular integro-differential equations, among oth.

Solitons, nonlinear evolution equations and inverse scattering M. Ablowitz, P. Clarkson It's very readable book and very important to every one who want to study more depthly about soliton theory via inverse scattering transform methods.

The Lax integrability of the coupled KdV equations derived from two-layer fluids [S.Y. Lou, B. Tong, H.C. Hu, X.Y. Tang, Coupled KdV equations derived from two-layer fluids, J. Phys.

A: Math. Gen. 39 () â] is investigated by means of prolongation by: Â There are at least two distinct integrable analogues of the CamassaâHolm equation in 2 + 1 dimensions [12, 15], For the two-peakon dynamics, the equations of motion are Fordy A P Prolongation structures of nonlinear evolution equations Soliton Theory: Cited by: () Time two-grid algorithm based on finite difference method for two-dimensional nonlinear fractional evolution equations.

Applied Numerical Mathematics() Superconvergence analysis of two-grid FEM for Maxwellâs equations with a thermal by: [9] Dryuma V.S., Non-linear multi-dimensional equations related to commuting vector fields, and their integration, In: International Conference âDifferential Equations and Related Topicsâ dedicated to I.G.

Petrovskii, XXII Joint Session of Moscow Mathematical Society and Petrovskii Seminar, Moscow, May 21â26, Moscow State University, Solitons, Nonlinear Evolution Equations and Inverse Scattering. This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

(not yet rated) 0 with reviews - Be the first. Solitons. Evolution equations, Nonlinear. The prolongation structures of a class of nonlinear evolution equations.

Dodd; and J. Gibbon; Published: 17 March Page(s): On the interactions between large-scale structure and finegrained turbulence in a free shear flow II.

The development of spatial. We study a nonlinear evolution partial differential equation, namely, the (2+1)-dimensional Boussinesq equation. For the first time Lie symmetry method together with simplest equation method is used to find the exact solutions of the (2+1)-dimensional Boussinesq equation.

Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1 Cited by: 6. The results of investigation show that the rogue wave can be generated by extreme behavior of homoclinic breather wave in higher dimensional nonlinear wave equations.

Two papers in our special issue are concerned about the study of application to the bifurcation approach of dynamical system on solving nonlinear evolution : Weiguo Rui, Wen-Xiu Ma, Chaudry Masood Khalique, Zuo-nong Zhu.

KadomtsevâPetviashvili equation Gino Biondini and Dmitry E. Pelinovsky Scholarpedia, vol.3 n (), revision # The Kadomtsev-Petviashvili equation(or simply the KP equation) is a nonlinear partial differential equation in two spatial and one temporal coordinate which describes the evolution of nonlinear, long waves of small.

() Symmetry-breaking bifurcation in O(2)ĂO(2)-symmetric nonlinear large problems and its application to the KuramotoâSivashinsky equation in two spatial dimensions.

Chaos, Solitons & FractalsCited by: Nonlinear algebraic equations, which are also called polynomial equations, are defined by equating polynomials (of degree greater than one) to zero. For example, + â. For a single polynomial equation, root-finding algorithms can be used to find solutions to the equation (i.e., sets of values for the variables that satisfy the equation).

However, systems of algebraic equations are more. On the different types of global and local conservation laws for partial differential equations in three spatial dimensions e-print archive arXiv; S.C.

Anco and Z. Yuzbasi+, Nonlinear integrable systems of Burgers type, Airy type, and Schrodinger type from elastic null curve flows in 3-dimensional Minkowski space.

The behaviour of many systems in chemistry, combustion and biology can be described using nonlinear reaction diffusion equations. Here, we use nonclassical symmetry techniques to analyse a class of nonlinear reaction diffusion equations, where both the diffusion coefficient and the coefficient of the reaction term are spatially dependent.

We construct new exact group invariant solutions for Cited by: 3. @article{osti_, title = {Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity}, author = {Ofman, L. and Morrison, P.J.

and Steinolfson, R.S.}, abstractNote = {The nonlinear evolution of the tearing mode instability with equilibrium shear flow is investigated via numerical solutions of the resistive magnetohydrodynamic equations.

solutions of the associated nonlinear evolution equations, but also many of the features of these evolution equations, e.g. Miura transformations, linear scattering problems, Backlund transformations, and integrable discretizations.

The method has the advantage that different evolution equations can be treated in a comprehensive and unifying way. A straightforward algorithm for the symbolic computation of generalized (higherâorder) symmetries of nonlinear evolution equations and lattice equations is presented.

The scaling properties of the evolution or lattice equations are used to determine the polynomial form of the generalized symmetries. The coefficients of the symmetry can be found by solving a linear system. The method. We discuss the asymptotic behavior of solutions of weakly coupled parabolic equations describing systems undergoing diffusion, convection and nonlinear interaction in a bounded spatial Cited by: Reactionâdiffusion systems are mathematical models which correspond to several physical phenomena.

The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.