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An elementary proof of the existence of monotone traveling waves solutions in a generalized Klein–Gordon equation
Author(s) -
Gomez Adrian,
Morales Nolbert,
Zamora Manuel
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7446
Subject(s) - mathematics , monotone polygon , uniqueness , traveling wave , mathematical analysis , type (biology) , nonlinear system , ordinary differential equation , klein–gordon equation , differential equation , mathematical physics , geometry , physics , quantum mechanics , ecology , biology
We analyze the existence and uniqueness of monotone traveling wavefront for a generalized nonlinear Klein–Gordon model∂ 2 ϕ ∂ t 2− p +∂ ϕ ∂ x2∂ 2 ϕ ∂ x 2+ V ′ ( ϕ ) = 0 , using classical arguments of ordinary differential equations, with V ( x ) a potentials family containing the ϕ ‐four potential V ( x ) = M 0( 1 − x 2 ) 2and the sine‐Gordon‐type potential V ( x ) = ( 1 / 2 ) ( 1 + cos ( π x ) ) . Also for these specific potentials, we give estimations of their monotone kink and anti‐kink solutions.