Heat conduction dynamics: a study of lie symmetry, solitons, and modulation instability
Rendiconti lincei. Scienze fisiche e naturali,
Год журнала:
2025,
Номер
unknown
Опубликована: Фев. 5, 2025
Язык: Английский
The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model
Mathematics,
Год журнала:
2024,
Номер
12(17), С. 2772 - 2772
Опубликована: Сен. 7, 2024
This
paper
is
concerned
with
the
novel
exact
solitons
for
truncated
M-fractional
(1+1)-dimensional
nonlinear
generalized
Bretherton
model
arbitrary
constants.
used
to
explain
resonant
interaction
between
waves
in
different
phenomena,
including
fluid
dynamics,
plasma
physics,
ocean
waves,
and
many
others.
A
series
of
solitons,
bright,
dark,
periodic,
singular,
singular–bright,
singular–dark,
other
are
obtained
by
applying
extended
sinh-Gordon
equation
expansion
(EShGEE)
modified
(G′/G2)-expansion
techniques.
definition
fractional
derivative
provides
solutions
that
distinct
from
previous
solutions.
Mathematica
software
was
obtain
verify
The
shown
through
2D,
3D,
density
plots.
stability
process
conducted
accurate.
Modulation
instability
determine
steady-state
results
corresponding
equation.
Язык: Английский
Multiple rogue wave, double-periodic soliton and breather wave solutions for a generalized breaking soliton system in (3 + 1)-dimensions
Scientific Reports,
Год журнала:
2024,
Номер
14(1)
Опубликована: Авг. 25, 2024
We
focused
on
solitonic
phenomena
in
wave
propagation
which
was
extracted
from
a
generalized
breaking
soliton
system
(3
+
1)-dimensions.
The
model
describes
the
interaction
between
Riemann
and
long
via
two
space
variable
nonlinear
media.
Abundant
double-periodic
soliton,
breather
multiple
rogue
solutions
to
by
Hirota
bilinear
form
mixture
of
exponentials
trigonometric
functions
are
presented.
Periodic-soliton,
periodic
studied
with
usage
symbolic
computation.
In
addition,
computation
applied
methods
for
governing
investigated.
Through
three-dimensional
graph,
density
two-dimensional
design
using
Maple,
physical
features
explained
all
right.
findings
demonstrate
investigated
model's
broad
variety
explicit
solutions.
All
outcomes
this
work
necessary
understand
meaning
behavior
explored
results
shed
light
significance
investigation
several
sciences
engineering.
Язык: Английский
Stability analysis, modulation instability, and the analytical wave solitons to the fractional Boussinesq-Burgers system
Physica Scripta,
Год журнала:
2024,
Номер
99(12), С. 125235 - 125235
Опубликована: Ноя. 2, 2024
Abstract
The
research
is
concerned
with
the
novel
analytical
solitons
to
(1+1)-D
nonlinear
Boussinesq-Burgers
System
(B-B
S)
in
sense
of
a
new
definition
fractional
derivatives.
system
helpful
describes
waves
different
phenomenons,
including
proliferation
shallow
water,
oceanic
and
many
others.
Authors
gain
solutions
involving
trigonometric,
hyperbolic,
rational
functions
by
using
exp
function
extended
sinh-Gordon
equation
expansion
(EShGEE)
methods.
Fractional
derivative
provides
better
results
than
present
results.
These
are
useful
areas
applied
sciences,
optical
fibers,
telecommunications,
plasma
physics,
fluid
dynamics
more.
shown
2-dimensional,
3-dimensional,
contour
graphs.
further
studies
governing
model.
stability
process
performed
verify
that
exact
accurate.
modulation
instability
used
determine
steady-state
stable
equation.
techniques
utilized
both
simple
effective.
Язык: Английский
Investigation of exact solitons to the quartic Rosenau-Kawahara-Regularized-Long-Wave fluid model with fractional derivative and qualitative analysis
Physica Scripta,
Год журнала:
2024,
Номер
100(1), С. 015270 - 015270
Опубликована: Дек. 11, 2024
Abstract
In
this
research,
the
exact
solitons
to
an
important
wave
equation,
namely,
quartic
Rosenau-Kawahara-Regularized-Long-Wave
(QRKRLW)
equation
are
obtained
along
with
effective
definition
of
fractional
derivative,
Truncated
M-fractional.
This
model
has
much
importance
in
fluid
dynamics,
shallow
waves,
and
many
others.
For
our
purpose,
two
schemes,
modified
extended
tanh
function
scheme
improved
(
G
′
/
stretchy="false">)
−
expansion
utilized.
As
a
consequence,
various
solutions
including,
singular,
singular-bright,
periodic,
dark,
dark-bright,
others
obtained.
To
verify
represent
solutions,
we
plotted
through
2D,
3D,
contour
plots
using
Mathematica
tool.
Additionally,
qualitative
analysis
concept
stability
modulation
instability
is
performed
for
verifying
being
accurate
solutions.
At
end,
schemes
also
useful
other
nonlinear
models
branches
sciences,
engineering.
Язык: Английский
Exploring New Traveling Wave Solutions to the Nonlinear Integro-Partial Differential Equations with Stability and Modulation Instability in Industrial Engineering
Computation,
Год журнала:
2024,
Номер
12(8), С. 161 - 161
Опубликована: Авг. 9, 2024
In
this
research
article,
we
demonstrate
the
generalized
expansion
method
to
investigate
nonlinear
integro-partial
differential
equations
via
an
efficient
mathematical
for
generating
abundant
exact
solutions
two
types
of
applicable
models.
Moreover,
stability
analysis
and
modulation
instability
are
also
studied
models
in
present
investigation.
These
analyses
have
several
applications
including
analyzing
control
systems,
engineering,
biomedical
neural
networks,
optical
fiber
communications,
signal
processing,
imaging
techniques,
oceanography,
astrophysical
phenomena.
To
study
PDEs
analytically,
traveling
wave
high
demand.
paper,
(1
+
1)-dimensional
integro-differential
Ito
equation
(IDIE),
relevant
various
branches
physics,
statistical
mechanics,
condensed
matter
quantum
field
theory,
dynamics
complex
etc.,
(2
Sawda–Kotera
(IDSKE),
providing
insights
into
physical
fields,
especially
gravity
conformal
investigated
obtain
a
variety
modern
physics
by
using
mentioned
method.
Since
give
us
vast
information
about
phenomena
models,
our
aims
determine
different
integrable
ordinary
equation.
Furthermore,
characteristics
obtained
new
been
illustrated
some
figures.
The
used
here
is
candid,
convenient,
proficient,
overwhelming
compared
other
existing
computational
techniques
solving
current
world
problems.
This
article
provides
exemplary
practice
finding
analytical
equations.
Язык: Английский
Computational study of thin films made from the ferroelectric materials with Paul Painlevé approach and expansion and variational methods
Scientific Reports,
Год журнала:
2024,
Номер
14(1)
Опубликована: Ноя. 23, 2024
In
this
paper,
the
thin-film
ferroelectric
material
equation
which
enables
a
propagation
of
solitary
polarization
in
materials,
and
it
also
can
be
described
using
nonlinear
evolution
equations.
Ferroelectrics
are
dielectric
materials
explain
wave
behaviors.
Thin
films
made
from
used
various
modern
electronics
devices.
The
Paul-Painlevé
approach
is
adopted
for
first
time
to
solve
these
analytically.
To
investigate
characterizations
new
waves,
dynamics
obtained
standard
$$\tan
(\phi
/2)$$
-expansion
technique
generalized
G-expansion
method.
bright
periodic
solutions
by
semi-inverse
variational
principle
scheme.
Many
alternative
responses
achieved
utilizing
formulaes;
each
shown
distinct
graph.
validity
such
methods
demonstrated
assessing
how
well
relevant
techniques
match
up.
Three
novel
analytical
numerical
provide
new,
dependable
approaches
determining
estimating
responses.
effect
free
variables
on
behavior
reached
few
graphs
exact
explored
depending
upon
nature
nonlinearities.
simulations,
exhibited
both
two-dimensional
(2D)
three-dimensional
(3D),
depict
solution
natural
digital
worlds.
These
findings
demonstrate
that
strategy
most
effective
way
mathematical
physics
problems.
Язык: Английский