# On the orbital stability of Gaussian solitary waves in the log-KdV equation

@article{Carles2014OnTO, title={On the orbital stability of Gaussian solitary waves in the log-KdV equation}, author={R{\'e}mi Carles and Dmitry E. Pelinovsky}, journal={Nonlinearity}, year={2014}, volume={27}, pages={3185 - 3202} }

We consider the logarithmic Korteweg–de Vries (log-KdV) equation, which models solitary waves in anharmonic chains with Hertzian interaction forces. By using an approximating sequence of global solutions of the regularized generalized KdV equation in with conserved L2 norm and energy, we construct a weak global solution of the log-KdV equation in a subset of . This construction yields conditional orbital stability of Gaussian solitary waves of the log-KdV equation, provided that uniqueness and…

## 16 Citations

### On the linearized log-KdV equation

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- 2016

The logarithmic KdV (log-KdV) equation admits global solutions in an energy space and exhibits Gaussian solitary waves. Orbital stability of Gaussian solitary waves is known to be an open problem. We…

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In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work \cite{carles}, in which the…

### Asymptotic stability of viscous shocks in the modular Burgers equation

- MathematicsNonlinearity
- 2021

Dynamics of viscous shocks is considered in the modular Burgers equation, where the time evolution becomes complicated due to singularities produced by the modular nonlinearity. We prove that the…

### The Gaussian soliton in the Fermi–Pasta–Ulam chain

- MathematicsNonlinear Dynamics
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We consider a Fermi–Pasta–Ulam (FPU) chain with the homogeneous fully nonlinear interaction potential which describes the propagation of acoustic wave in chains of touching beads without…

### On a class of solutions to the generalized KdV type equation

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We consider the IVP associated to the generalized KdV equation with low degree of nonlinearity [Formula: see text] By using an argument similar to that introduced by Cazenave and Naumkin [Local…

### Orbital stability of periodic standing waves for the logarithmic Klein-Gordon equation

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### Well-Posedness and Orbital Stability of Periodic Traveling Waves for Schamel's Equation

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- 2018

In this paper we will prove results of global well-posedness and orbital stability of periodic traveling-wave solutions related to the Schamel equation. The global solvability will be established by…

### Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

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Abstract We consider the Schrödinger equation with a nondispersive logarithmic nonlinearity and a repulsive harmonic potential. For a suitable range of the coefficients, there exist two positive…

### Existence and multiplicity of solutions for logarithmic Schrödinger equations with potential

- Mathematics
- 2021

We study the logarithmic Schrodinger equation with the sign-changing potential function. It is known that the corresponding functional is not well defined in H1(RN), but by imposing some condition on…

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