TITLE

# Solitary wave interaction for a higher-order nonlinear SchrÃ¶dinger equation

AUTHOR(S)
HOSEINI, S. M.; MARCHANT, T. R.
PUB. DATE
April 2007
SOURCE
IMA Journal of Applied Mathematics;Apr2007, Vol. 72 Issue 2, p206
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Solitary wave interaction for a higher-order version of the nonlinear SchrÃ¶dinger (NLS) equation is examined. An asymptotic transformation is used to transform a higher-order NLS equation to a higher-order member of the NLS integrable hierarchy, if an algebraic relationship between the higher-order coefficients is satisfied. The transformation is used to derive the higher-order one- and two-soliton solutions; in general, the N-soliton solution can be derived. It is shown that the higher-order collision is asymptotically elastic and analytical expressions are found for the higher-order phase and coordinate shifts. Numerical simulations of the interaction of two higher-order solitary waves are also performed. Two examples are considered, one satisfies the algebraic relationship derived from asymptotic theory, and the other does not. For the example which satisfies the algebraic relationship, the numerical results confirm that the collision is elastic. The numerical and theoretical predictions for the higher-order phase and coordinate shifts are also in strong agreement. For the example which does not satisfy the algebraic relationship, the numerical results show that the collision is inelastic and radiation is shed by the solitary wave collision. As the bed of radiation shed by the waves decays very slowly (like tâˆ’Â½), it is computationally infeasible to calculate the final phase and coordinate shifts for the inelastic example. An asymptotic conservation law is derived and used to test the finite-difference scheme for the numerical solutions.
ACCESSION #
44587418

## Related Articles

• Concordance method of asymptotic expansions in a singularly-perturbed boundary-value problem for the laplace operator. Gadyl'shin, R. // Journal of Mathematical Sciences;Feb2005, Vol. 125 Issue 5, p579

In this paper, the concordance method of asymptotic expansions is demonstrated by examining the construction of asymptotics with respect to a small parameter of eigenvalues of the Dirichlet problem for the Laplace operator in ann-dimensional bounded domain with a thin cylindrical appendix of...

• ASYMPTOTIC SEMIVALUES AND A SHORT PROOF OF KANNAI'S THEOREM. Dubey, Pradeep // Mathematics of Operations Research;May80, Vol. 5 Issue 2, p267

Generalizations of the Shapley value, called semivalues, are introduced. We consider their asymptotic behavior for sequences of games that approach a nonatomic game, and show that limiting semivalues exist on pNA. In the process a short proof of Kannai's asymptotic theorem for the Shapley value...

• Apollonius' problem.  // Hutchinson Dictionary of Scientific Biography;2005, p1

Problem set by Apollonius of Perga, to describe a circle touching three other given circles.

• Investigating Horizontal Asymptotes and the Graphs of Rational Functions. Slavens, Dawn; Harrell, Marvin // Ohio Journal of School Mathematics;Autumn2006, Issue 54, p38

The article presents an activity related to horizontal asymptotes and the graphs of rational functions. It is associated to the activity "Investigating Vertical Asymptotes and the Graph of Rational Functions" that was published in a 2004 issue of "Ohio Journal of School Mathematics." A rational...

• HEAT CONTENT ASYMPTOTICS FOR PLANAR REGIONS WITH CUSPS. VAN DEN BERG, M. // Journal of the London Mathematical Society;06/01/1998, Vol. 57 Issue 3, p677

Asymptotic results are given for the heat content of planar regions with cusps.

• A Note on the Complexity of Real Algebraic Hypersurfaces. Kerber, Michael; Sagraloff, Michael // Graphs & Combinatorics;May2011, Vol. 27 Issue 3, p419

Given an algebraic hypersurface \$\${\fancyscript{O}}\$\$ in \$\${\mathbb{R}^d}\$\$, how many simplices are necessary for a simplicial complex isotopic to \$\${\fancyscript{O}}\$\$? We address this problem and the variant where all vertices of the complex must lie on \$\${\fancyscript{O}}\$\$. We give...

• Histogram Based Circle Detection. Basalamah, Saleh // International Journal of Computer Science & Network Security;Aug2012, Vol. 12 Issue 8, p40

Circle detection is important for many applications. We propose a method for circle detection using a histogram based accumulator space. Our method uses a single accumulator space to find different size circles. It is tested to be robust and able to detect partial circles or circles in partial...

• On the Whewell Parametrization of the Euler Elastica. Mladenov, I. M.; Hadzhilazova, M. Ts.; Djondjorov, P. A.; Vassilev, V. M. // AIP Conference Proceedings;11/30/2009, Vol. 1191 Issue 1, p133

Starting from first principles, the curvature of the plane elastic line is expressed in terms of the slope of its tangent. This is used further for finding its intrinsic equation and for deriving a new explicit parametrization of the Euler elastica.

• Qualitative analysis of classes of motion for multiresonant systems I. An algebraic method. Luongo, A.; Di Egidio, A.; Paolone, A. // Acta Mechanica;Jan2005, Vol. 174 Issue 1/2, p91

A general multiresonant system is considered, in which the linear frequency and, possibly, a forcing frequency are involved in a set of linear conditions. The nature of the resonances is first discussed, by distinguishingindependentanddependentequations, and both theanalysisanddesignproblems of...

Share