What does this research mean for the field?

Specific necessary and sufficient conditions govern the stability of soliton solutions to fourth-order nonlinear Schrödinger equations with arbitrary power nonlinearities, which also dictate the stabilization of self-focusing and collapse by high-order dispersion. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to determine the conditions for the stability of soliton solutions in fourth-order nonlinear Schrödinger equations.

February 1, 1996Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Stabilization of soliton instabilities by higher-order dispersion: Fourth-order nonlinear Schrödinger-type equations

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Authors

VKV. I. KarpmanHebrew College

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Implication

Randomized trial studies soliton stability in nonlinear equations, suggesting new stabilization methods.

Key Points

This research aims to determine the conditions for the stability of soliton solutions in fourth-order nonlinear Schrödinger equations.
Analyzed soliton solutions in different space dimensions.
Identified necessary and sufficient conditions for stability against small perturbations.
Studied the effects of high-order dispersion on self-focusing and collapse.
Found specific conditions that ensure stability of soliton solutions under perturbations.
Results indicate that higher-order dispersion can stabilize self-focusing and prevent collapse.

Cite This Study

V. I. Karpman (1996) studied this question.

synapsesocial.com/papers/6a64a156609ed84cb3070eac https://doi.org/10.1103/physreve.53.r1336

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Stabilization of soliton instabilities by higher-order dispersion: Fourth-order nonlinear Schrödinger-type equations

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Key Points

Cite This Study

Stabilization of soliton instabilities by higher-order dispersion: Fourth-order nonlinear Schrödinger-type equations

Discussion

Member takes

Implication

Key Points

Cite This Study

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