# Properties of synchronous collisions of solitons in the Korteweg-de Vries equation

@article{Tarasova2022PropertiesOS, title={Properties of synchronous collisions of solitons in the Korteweg-de Vries equation}, author={Tatiana Tarasova and Alexey Slunyaev}, journal={Commun. Nonlinear Sci. Numer. Simul.}, year={2022}, volume={118}, pages={107048} }

## One Citation

### Statistical properties of extreme soliton collisions.

- PhysicsChaos
- 2022

Synchronous collisions between a large number of solitons are considered in the context of a statistical description. It is shown that, during the interaction of solitons of the same signs, the wave…

## 39 References

### Strongly interacting soliton gas and formation of rogue waves

- PhysicsPhysical Review E
- 2018

We study numerically the properties of (statistically) homogeneous soliton gas depending on soliton density (proportional to number of solitons per unit length) and soliton velocities, in the…

### Role of Multiple Soliton Interactions in the Generation of Rogue Waves: The Modified Korteweg-de Vries Framework.

- PhysicsPhysical review letters
- 2016

The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation, when solitons possess "frozen" phases (certain polarities).

### KDV Soliton Gas: Interactions and Turbulence

- Physics
- 2017

The collective behavior of soliton ensemble corresponded to soliton turbulence is studied within the integrable Korteweg–de Vries (KdV) equation. Two-soliton interactions play a definitive role in…

### On the optimal focusing of solitons and breathers in long‐wave models

- PhysicsStudies in Applied Mathematics
- 2019

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation (GE) with positive cubic nonlinearity, which in the…

### Large-Order Asymptotics for Multiple-Pole Solitons of the Focusing Nonlinear Schrödinger Equation

- MathematicsJ. Nonlinear Sci.
- 2019

It is proved that in a local scaling the solitons converge to functions satisfying the second member of the Painlevé-III hierarchy in the sense of Sakka, a generalization of a function recently identified by Suleimanov in the context of geometric optics.

### Soliton synchronization in the focusing nonlinear Schrödinger equation.

- PhysicsPhysical review. E
- 2016

It is shown thatsoliton synchronization can be achieved by synchronizing the asymptotic middle states of the solitons, and conditions of soliton synchronization in terms of thesolitons' position and phase parameters are given.

### Generalized hydrodynamics of the KdV soliton gas

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2022

We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for…

### Numerical modeling of soliton turbulence within the focusing Gardner equation: Rogue wave emergence

- Physics
- 2019

### Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions

- MathematicsJ. Nonlinear Sci.
- 2011

It is proved that the class of N-component ‘cold-gas’ hydrodynamic reductions represent integrable linearly degenerate hydrod dynamic type systems for arbitrary N which is a strong evidence in favour of integrability of the full kinetic equation.

### Kinetic equation for a dense soliton gas.

- Physics, MathematicsPhysical review letters
- 2005

The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions and reduces to a transport of the eigenvalues of the associated spectral problem with the corresponding soliton velocities modified by the collisions.