Interaction of solitary pulses in active dispersive-dissipative media

被引：14
作者：
Tseluiko, Dmitri [1 ]
Saprykin, Sergey [1 ]
Kalliadasis, Serafim [1 ]
机构：
[1] Univ London Imperial Coll Sci Technol & Med, Dept Chem Engn, London SW7 2AZ, England
来源：
PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES | 2010年 / 59卷 / 02期
关键词：
dissipative solitons; solitary-pulse interaction; bound states; generalized Kuramoto-Sivashinsky equation; WAVES; INSTABILITY; STABILITY; SYSTEM; FILM;
D O I：
10.3176/proc.2010.2.12
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We examine weak interaction and formation of bound states of pulses for the generalized Kuramoto-Sivashinsky (gKS) equation, which is one of the simplest prototypes describing active media with energy supply, dissipation, dispersion, and nonlinearity. We derive a system of ordinary differential equations describing the leading-order dynamics of the pulses of the gKS equation and prove a criterion for the existence of a countable infinite or finite number of bound states. Our theory is corroborated by computations of the full equation.
引用
收藏
页码：139 / 144
页数：6
相关论文
共 18 条
  • [1] Weak interaction of solitary pulses in active dispersive-dissipative nonlinear media
    Tseluiko, Dmitri
    Kalliadasis, Serafim
    IMA JOURNAL OF APPLIED MATHEMATICS, 2014, 79 (02) : 274 - 299
  • [2] Linearly implicit schemes for a class of dispersive-dissipative systems
    Akrivis, Georgios
    Smyrlis, Yiorgos-Sokratis
    CALCOLO, 2011, 48 (02) : 145 - 172
  • [3] A geometric construction of traveling waves in a generalized nonlinear dispersive-dissipative equation
    Mansour, M. B. A.
    JOURNAL OF GEOMETRY AND PHYSICS, 2013, 69 : 116 - 122
  • [4] COHERENT STRUCTURES IN NONLOCAL DISPERSIVE ACTIVE-DISSIPATIVE SYSTEMS
    Lin, Te-Sheng
    Pradas, Marc
    Kalliadasis, Serafim
    Papageorgiou, Demetrios T.
    Tseluiko, Dmitri
    SIAM JOURNAL ON APPLIED MATHEMATICS, 2015, 75 (02) : 538 - 563
  • [5] A NOTE ON THE DISPERSIVE-DISSIPATIVE WAVE EQUATION HAVING STRONG DAMPING AND NONLINEAR SOURCES
    Liu, Mengyao
    Liu, Bingchen
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2025, 24 (01) : 100 - 124
  • [6] Local stability theory of solitary pulses in an active medium
    Chang, HC
    Demekhin, EA
    Kopelevich, DI
    PHYSICA D, 1996, 97 (04): : 353 - 375
  • [7] Dissipative pulses stabilized by nonlinear gradient terms: A review of their dynamics and their interaction
    Descalzi, Orazio
    Facao, M.
    Carvalho, M. I.
    Cartes, Carlos
    Brand, Helmut R.
    PHYSICA D-NONLINEAR PHENOMENA, 2025, 473
  • [8] FINITE TIME BLOW-UP FOR THE NONLINEAR FOURTH-ORDER DISPERSIVE-DISSIPATIVE WAVE EQUATION AT HIGH ENERGY LEVEL
    Xu Runzhang
    Yang Yanbing
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2012, 23 (05)
  • [9] On the Dissipative Complex Ginzburg-Landau Equation Governing the Propagation of Solitary Pulses in Dissipative Nonlinear Transmission Lines
    Kengne, E.
    Tadmon, C.
    Vaillancourt, R.
    CHINESE JOURNAL OF PHYSICS, 2009, 47 (01) : 80 - 91
  • [10] Propagation of chirped rectangular pulses in dispersive media: analytical analysis
    Granot, Er'El
    OPTICS LETTERS, 2019, 44 (19) : 4745 - 4748
12