Construction of 2-solitons with logarithmic distance for the one-dimensional cubic Schrödinger system

Martel, Yvan; Nguyễn, Tiến Vinh

doi:10.3934/dcds.2020087

Cited by 8 publications

(3 citation statements)

References 29 publications

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“…As [1], there are several results about multisolitary waves with logarithmic distance; see e.g. [18,36,37,38]. We note that for the damped nonlinear Klein-Gordon equation, multi-solitary waves of (DNKG) are impossible to move at a constant speed by the damping α.…”

Section: Previous Resultsmentioning

confidence: 80%

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Kenjiro

Nakanishi

2022

Ann. PDE

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We consider the damped nonlinear Klein-Gordon equation with a delta potential, where p > 2, α > 0, γ < 2, and δ 0 = δ 0 (x) denotes the Dirac delta with the mass at the origin. When γ = 0, Côte, Martel and Yuan [7] proved that any global solution either converges to 0 or to the sum of K ≥ 1 decoupled solitary waves which have alternative signs. In this paper, we first prove that any global solution either converges to 0 or to the sum of K ≥ 1 decoupled solitary waves. Next we construct a single solitary wave solution that moves away from the origin when γ < 0 and construct an even 2-solitary wave solution when γ ≤ −2. Last we give single solitary wave solutions and even 2-solitary wave solutions an upper bound for the distance between the origin and the solitary wave.

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Section: Previous Resultsmentioning

confidence: 80%

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Kenjiro

Nakanishi

2022

Ann. PDE

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“…where μ > 0, α, v ∈ R. Of course, system (1.3) with ψ 2 = 0 (or ψ 1 = 0) reduces to the usual NLS equation, hence we can also generate test solutions for the corresponding system (see also [27]). Now, let us consider the more general cNLS system with constant coefficients…”

Section: Some Results About the Nls System With Constant Coefficientsmentioning

confidence: 99%

Lie symmetry properties of the two-component complex Ginzburg–Landau system with variable coefficients

Güngör

Torres

2020

J. Phys. A: Math. Theor.

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We classify the Lie point symmetries of a system of nonlinearly coupled complex Ginzburg-Landau equations with time and space dependent potentials and nonlinearities. New families of systems with exact solutions and conservation laws are identified. When there is only space dependence, the system can be reduced to a set of ordinary differential equations for the amplitude and phase components, for which integrability and first integrals are discussed.

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“…(1) Nguyen [31] constructed double pole solution for both L 2 subcritical and L 2 supercritical generalized KdV equations; (2) Nguyen [32] constructed double pole solution for L 2 subcritical nonlinear Schrödinger equations; (3) Martel-Nguyen [26] constructed double pole solution for one dimensional cubic Schrödinger system.…”

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confidence: 99%

Strongly interacting multi-solitons for generalized Benjamin-Ono equations

Yang¹,

Wang²

2022

Preprint

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We consider the generalized Benjamin-Ono equation:with L 2 -supercritical power p > 3 or L 2 -subcritical power 2 < p < 3. We will construct strongly interacting multi-solitary wave of the form:, where n ≥ 2, and the parameters x i (t) satisfying x i (t)−x i+1 (t) ∼ α k √ t as t → +∞, for some universal positive constants α k . We will also prove the uniqueness of such solutions in the case of n = 2 and p > 3.

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Construction of 2-solitons with logarithmic distance for the one-dimensional cubic Schrödinger system

Abstract: = 0where Qc(x) = cQ(cx) and Ωc > 0 is a constant. Such logarithmic regime with nonsymmetric solitons does not exist in the integrable cases ω = 0 and ω = 1 and is still unknown in the non-integrable scalar case.

Cited by 8 publications

References 29 publications

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Global Dynamics Around 2-Solitons for the Nonlinear Damped Klein-Gordon Equations

Lie symmetry properties of the two-component complex Ginzburg–Landau system with variable coefficients

Strongly interacting multi-solitons for generalized Benjamin-Ono equations

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