# 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

- Physics, Mathematics
- 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…

### Orbital Stability of Periodic Waves for the Log-KdV Equation

- Mathematics
- 2014

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…

### Justification of the log-KdV Equation in Granular Chains: The Case of Precompression

- MathematicsSIAM J. Math. Anal.
- 2014

For travelling waves with nonzero boundary conditions, we justify the logarithmic Korteweg-de Vries equation as the leading approximation of the Fermi-Pasta-Ulam lattice with Hertzian nonlinear…

### Existence and stability of a two-parameter family of solitary waves for a logarithmic NLS–KdV system

- MathematicsNonlinear Analysis
- 2019

### 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
- 2021

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

- MathematicsCommunications in Contemporary Mathematics
- 2019

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

- Mathematics
- 2019

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

- Mathematics
- 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…

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