Dissipative solitons

DOI10.1016/0167-2789(95)00111-GzbMath0885.35108OpenAlexW2913558729MaRDI QIDQ1896546

Christo I. Christov, Manuel G. Velarde

Publication date: 29 August 1995

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(95)00111-g

zbMATH Keywords

Kuramoto-Sivashinsky equationkinkscollisionshocksKorteweg-de Vries equationsboreshydraulic jumpsKdV sechesproduction-dissipation energy balanceZubusky and Kruskal's soliton concept

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Soliton equations (35Q51)

Related Items

A high-order implicit–explicit Runge–Kutta type scheme for the numerical solution of the Kuramoto–Sivashinsky equation, Waves in microstructured solids and the Boussinesq paradigm, Solitary wave interactions and reshaping in coupled systems, Dissipative acoustic solitons under a weakly-nonlinear, Lagrangian-averaged Euler-\(\alpha\) model of single-phase lossless fluids, DISPERSIVE EFFECTS IN A MODIFIED KURAMOTO–SIVASHINSKY EQUATION, DISSIPATIVE SOLITONS AND COMPLEX CURRENTS IN ACTIVE LATTICES, Destabilization of Localized Structures in Reaction-Diffusion Systems Induced by Delayed Feedback, Three-dimensional localized coherent structures of surface turbulence. II. Λ solitons, Dissipative solitons for bistable delayed-feedback systems, Single and multi-vertices solitons in lattices of active Morse-van der Pol units, The coupled Kuramoto-Sivashinsky-KdV equations for surface wave in multilayered liquid films, Pulse dynamics in low-Reynolds-number interfacial hydrodynamics: experiments and theory, A geometric construction of traveling waves in a generalized nonlinear dispersive-dissipative equation, Persistence of kink and periodic waves to singularly perturbed two-component Drinfel'd-Sokolov-Wilson system, Well-posedness results and dissipative limit of high dimensional KdV-type equations, Stability of solution of Kuramoto-Sivashinsky-Korteweg-de Vries system, \(H^1\) solutions for a Kuramoto-Velarde type equation, Numerical simulation of propagation of solitary deformation waves in a compressible hyperelastic rod, Emergence of Solitonic Structures in Hierarchical Korteweg–de Vries Systems, Acoustic traveling waves in thermoviscous perfect gases: kinks, acceleration waves, and shocks under the Taylor-Lighthill balance, Description of kink evolution by means of particular analytical solutions, Asymptotic attractors of KdV-KSV equations, Dynamics of a reactive falling film at large Péclet numbers. I. Long-wave approximation, Two-dimensional wave dynamics in thin films. I. Stationary solitary pulses, 2D solitons in Boussinesq equation with dissipation, Numerical Simulation of Interaction of Solitons and Solitary Waves in Granular Materials, Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms, Solitary waves in turbulent open-channel flow, Physical dynamics of quasi-particles in nonlinear wave equations, Drift bifurcation of dissipative solitons due to a change of shape: experiment and theory, Propagation of \(sech^2\)-type solitary waves in hierarchical KdV-type systems, Three Sources and Three Component Parts of the Concept of Dissipative Solitons, Solitons in Viscous Flows, Anharmonic Oscillations, Dissipative Solitons and Non-Ohmic Supersonic Electric Transport, Dispersive-dissipative solitons in nonlinear solids., Exact periodic solutions of the complex Ginzburg–Landau equation, Near-critical turbulent open-channel flows over bumps and ramps, The effects of generalized dispersion on dissipative dynamical systems, Interaction of counterpropagation hot spots in solid fuel combustion, Global solutions for coupled Kuramoto-Sivashinsky-KdV system, Electrohydrodynamic instability of viscous liquid films: electrostatically modified second-order Benney and Kuramoto-Sivashinsky models, Well-posedness result for the Kuramoto-Velarde equation, Snake solitons in the cubic-quintic Ginzburg-Landau equation, COHERENT MOTIONS AND CLUSTERS IN A DISSIPATIVE MORSE RING CHAIN, DISSIPATIVE QUASI-PARTICLES: THE GENERALIZED WAVE EQUATION APPROACH, Interaction of solitons in a Boussinesq equation with dissipation, GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE CAUCHY PROBLEM OF A DISSIPATIVE BOUSSINESQ-TYPE EQUATION, Periodic solutions of the non-integrable convective fluid equation, Peakompactons: Peaked compact nonlinear waves, Strong dispersive effects on internal nonlinear waves in a sheared, stably stratified fluid layer

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems
• Who cares about integrability?
• The Eckhaus instability for traveling waves
• Theory of nonlinear lattices.
• Laminarizing effects of dispersion in an active-dissipative nonlinear medium
• Cnoidal wave trains and solitary waves in a dissipation-modified Korteweg-de Vries equation
• Construction of stationary waves on a falling film
• On localization solutions of an equation governing Benard--Marangoni convection
• On solitary waves running down an inclined plane
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Wave formation in laminar flow down an inclined plane
• Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers
• Bénard–Marangoni convection with a deformable interface and poorly conducting boundaries
• Exact solitary waves in a convecting fluid
• Dissipative Korteweg–de Vries description of Marangoni–Bénard oscillatory convection
• Long waves on a thin fluid layer flowing down an inclined plane
• Nonlinear stability of a viscous film with respect to three-dimensional side-band disturbances
• INELASTIC INTERACTION OF BOUSSINESQ SOLITONS
• SOLITARY WAVES, SOLITON BOUND STATES AND CHAOS IN A DISSIPATIVE KORTEWEG-DE VRIES EQUATION
• FURTHER RESULTS ON THE EVOLUTION OF SOLITARY WAVES AND THEIR BOUND STATES OF A DISSIPATIVE KORTEWEG-DE VRIES EQUATION
• Method for Solving the Korteweg-deVries Equation
• Finite amplitude side-band stability of a viscous film
• A three-dimensional description of solitary waves and their interaction in Marangoni–Bénard layers
• On the van der Waals Theory of the Vapor-Liquid Equilibrium. I. Discussion of a One-Dimensional Model
• Long Waves on Liquid Films
• Occurrence of Finite-Amplitude Surface Waves on Falling Liquid Films
• Shallow Water Waves on a Viscous Fluid—The Undular Bore