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Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in a plasma or fluid
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Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in a plasma or fluid
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Journal Article
Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in a plasma or fluid
2019
Overview
Plasmas and fluids are of current interest, supporting a variety of wave phenomena. Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation for the nonlinear phenomena in a plasma or fluid. Based on the existing bilinear form,
N
-soliton solutions in the Gramian are derived, where
N
= 1, 2, 3…. With
N
= 3, three-soliton solutions are constructed. Fission and fusion for the three solitons are presented. Effects of the variable coefficients, i.e.
h
(
t
),
l
(
t
),
q
(
t
),
n
(
t
) and
m
(
t
), on the soliton fission and fusion are revealed: soliton velocity is related to
h
(
t
),
l
(
t
),
q
(
t
),
n
(
t
) and
m
(
t
), while the soliton amplitude cannot be affected by them, where
t
is the scaled temporal coordinate,
h
(
t
),
l
(
t
) and
q
(
t
) give the perturbed effects, and
m
(
t
) and
n
(
t
), respectively, stand for the disturbed wave velocities along two transverse spatial coordinates. We show the three parallel solitons with the same direction.
Publisher
The Royal Society Publishing
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