Explicit traveling waves and invariant algebraic curves

Armengol Gasull; Hector Giacomini

Explicit traveling waves and invariant algebraic curves

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Resum

We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.

Idioma original	Anglès
Pàgines (de-a)	1597-1606
Nombre de pàgines	10
Revista	Nonlinearity
Volum	28
Estat de la publicació	En premsa - 2015

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https://ddd.uab.cat/record/145355

Sistemas dinámicos contínuos y discretos: bifurcaciones, orbitas periódicas, integrabilidad y aplicaciones
Torregrosa i Arús, J. (PI), Cima Mollet, A. M. (Investigador/a), Gasull Embid, A. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Mañosa Fernández, V. (Investigador/a), Artes Ferragud, J. C. (Investigador/a), Llibre Salo, J. (Investigador/a), Corbera Subirana, M. (Investigador/a), Pantazi ., C. (Investigador/a), Garrido Pelaez, J. M. (Col.laborador/a), Mañosas Capellades, F. (Col.laborador/a), Jimenez Ruiz, J. J. (Col.laborador/a), Mayayo Cortasa, T. (Col.laborador/a) & Villadelprat Yague, J. (Investigador/a)
1/09/23 → 31/08/26
Projecte: Projectes i Ajuts a la Recerca

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title = "Explicit traveling waves and invariant algebraic curves",

abstract = "We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.",

keywords = "Algebraic invariant solution, Fischer-Kolmogorov equation, Partial differential equation, Polynomial differential equations, Travelling wave",

author = "Armengol Gasull and Hector Giacomini",

year = "2015",

language = "English",

volume = "28",

pages = "1597--1606",

journal = "Nonlinearity",

issn = "0951-7715",

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T1 - Explicit traveling waves and invariant algebraic curves

AU - Gasull, Armengol

AU - Giacomini, Hector

PY - 2015

Y1 - 2015

N2 - We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.

AB - We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.

KW - Algebraic invariant solution

KW - Fischer-Kolmogorov equation

KW - Partial differential equation

KW - Polynomial differential equations

KW - Travelling wave

M3 - Article

SN - 0951-7715

VL - 28

SP - 1597

EP - 1606

JO - Nonlinearity

JF - Nonlinearity

ER -

Explicit traveling waves and invariant algebraic curves

Resum

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Sistemas dinámicos contínuos y discretos: bifurcaciones, orbitas periódicas, integrabilidad y aplicaciones

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