Nonlinear Waves in Integrable and Nonintegrable Systems

Yang, Jianke

doi:10.1137/1.9780898719680

Cited by 921 publications

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“…Also, we use the algorithm of dpg form [36]. A useful book for constructive algorithms was written by Yang [34].…”

Section: E65mentioning

confidence: 99%

“…Also, the coupled nonlinear Schrödinger equations (cnlse) is obtained in a great variety of physical situations [33,34]. For example, in fiber system, such equations have been shown to govern pulse propagation along orthogonal polarization axes [10,11,19,24,33,34].…”

Section: Introductionmentioning

confidence: 99%

“…For example, in fiber system, such equations have been shown to govern pulse propagation along orthogonal polarization axes [10,11,19,24,33,34]. Also, these equations model beam propagation inside photo or crystals refractives as well as water wave effects [33,34]. Solitary waves are called vector solitons as they generally contain two parts.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to passing-through collision is an E53 important phenomena such that vector solitons also bounce off each other or trap each other. Solutions of this system have been studied intensively in recent years in numerical aspects and analytical [19,20,21,22,23,24,31,32,33,34,35,36,37]. Numerical examples were investigated by many authors in the one dimensional case [21,21,22,23,24,34].…”

Section: Introductionmentioning

confidence: 99%

“…We consider the example of the three dimensional coupled nonlinear Schrödinger equations (cnlse) [34]:…”

Section: Introductionmentioning

confidence: 99%

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The new streamline diffusion for the 3D coupled Schrodinger equations with a cross-phase modulation

Rostamy¹

2013

ANZIAMJ

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We study the new streamline diffusion finite element method for treating the three dimensional coupled nonlinear Schrödinger equation. We derive stability estimates and optimal convergence rates. Moreover, an a priori error estimate is obtained and we compare the corresponding optimal convergence rate for popular numerical methods such as conservative finite difference, semi-implicit finite difference, semi-discrete finite element and the time-splitting spectral method. We justify the advantage of the streamline diffusion method versus the some numerical methods with some examples. Test problems are presented to verify the efficiency and accuracy of the method. The results reveal that the proposed scheme is very effective, convenient and quite accurate for such considered problems rather than other methods.

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“…Also, we use the algorithm of dpg form [36]. A useful book for constructive algorithms was written by Yang [34].…”

Section: E65mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We consider the example of the three dimensional coupled nonlinear Schrödinger equations (cnlse) [34]:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The new streamline diffusion for the 3D coupled Schrodinger equations with a cross-phase modulation

Rostamy¹

2013

ANZIAMJ

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Stability of Dipole Gap Solitons in Two‐Dimensional Lattice Potentials

Dror¹,

Malomed²

2013

Nonlinear Physical Systems

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3D Nonlinear Localized Gap Modes in Bose‐Einstein Condensates Trapped by Optical Lattices and Space‐Periodic Nonlinear Potentials

Zhang

Zeng

2022

Advanced Photonics Research

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Optical lattices and Feshbach resonance management are two mighty and widely used techniques for studying, both experimentally and theoretically, various physical issues and the underlying nonlinear dynamics of Bose−Einstein condensates. Both techniques show great power for studying solitons of different types, and particularly, the former technique realizes the creation of 1D bright matter‐wave gap solitons, whose formation and properties in multidimensional systems, however, are much less known. Herein, both techniques and study are combined, theoretically and numerically, the formation and dynamics of 3D nonlinear localized gap modes, including fundamental gap solitons and their higher‐order ones as soliton clusters, as well as gap vortices with topological charge s = 1. The stability regions of all the localized gap modes are identified by means of direct perturbed numerical simulations, revealing important insights into soliton physics in multidimensional space.

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Nonlinear Waves in Integrable and Nonintegrable Systems

Cited by 921 publications

References 0 publications

The new streamline diffusion for the 3D coupled Schrodinger equations with a cross-phase modulation

The new streamline diffusion for the 3D coupled Schrodinger equations with a cross-phase modulation

Stability of Dipole Gap Solitons in Two‐Dimensional Lattice Potentials

3D Nonlinear Localized Gap Modes in Bose‐Einstein Condensates Trapped by Optical Lattices and Space‐Periodic Nonlinear Potentials

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