Scientific Reports,
Journal Year:
2024,
Volume and Issue:
14(1)
Published: Nov. 17, 2024
Solitary
wave
solutions
to
the
nonlinear
evolution
equations
have
recently
attracted
widespread
interest
in
engineering
and
physical
sciences.
In
this
work,
we
investigate
fractional
generalised
Pochhammer–Chree
equation
under
power-law
of
nonlinearity
with
order
m.
This
is
used
describe
longitudinal
deformation
propagation
an
elastic
rod.
study,
secured
a
variety
exact
solitary
by
assistance
developed
technique
known
as
modified
generalized
exponential
rational
function
method.
Exact
various
categories,
such
bright-dark,
bright,
mixed,
singular,
dark,
complex,
combined
solitons,
are
extracted.
The
applied
approach
highly
efficient
has
significant
computational
capability
efficiently
tackle
high
degree
accuracy
systems.
To
analyze
governing
system,
investigation
converted
ordinary
differential
through
application
suitable
transformation
$$\beta$$
-derivative.
addition
illustrate
behavior
solution
at
parameter
values,
generate
2D
3D
graphs
that
incorporate
pertinent
parameters.
Moreover,
Galilean
employed
sensitivity
analysis.
research's
results
potential
enhance
comprehension
dynamic
characteristics
displayed
defined
system
verify
efficacy
strategies
been
implemented.
obtained
substantial
contribution
science
fields
associated
higher
dimensions.
Open Physics,
Journal Year:
2024,
Volume and Issue:
22(1)
Published: Jan. 1, 2024
Abstract
In
this
work,
the
exact
solutions
of
(2+1)-dimensional
generalized
Hirota–Satsuma–Ito
equation
are
reported
by
adopting
He’s
variational
direct
technique
(HVDT).
The
analytic
findings
were
obtained
semi-inverse
scheme,
and
six
form
supposed
studies
reveal
that
belong
to
soliton
groups.
modulation
instability
is
considered.
tan(Πξ)
\tan
\left(\Pi
\left(\xi
))
scheme
on
suggested
model
employed
study
new
rational
solutions.
investigated
properties
determined
graphic
studies,
which
shows
significantly
values
parameters
susceptibility
abundant
results
in
work
expected
open
perspectives
for
traveling
wave
theory.
For
aforementioned
solutions,
we
graphically
describe
their
dynamical
properties.
It
worth
mentioning
our
not
only
enable
us
understand
dynamic
such
equations
more
intuitively
but
also
provide
some
ideas
researchers
facilitate
depth
exploration.
important
mention
proposed
method
highly
effective,
consistent,
impacting
can
be
utilized
solve
different
physical
models.
AIMS Mathematics,
Journal Year:
2024,
Volume and Issue:
9(10), P. 27403 - 27417
Published: Jan. 1, 2024
<p>This
study
explores
the
stochastic
Benjamin-Bona-Mahony
(BBM)
equation
with
a
beta
derivative
(BD),
thereby
incorporating
multiplicative
noise
in
Itô
sense.
We
derive
various
analytical
soliton
solutions
for
these
equations
utilizing
two
distinct
expansion
methods:
$
\frac{\mathcal{G}^{\prime}}{\mathcal{G}^{\prime}+\mathcal{G}+\mathcal{A}}
$-expansion
and
modified
\frac{\mathcal{G}^{\prime}}{\mathcal{G}^{2}}
techniques,
both
within
framework
of
derivatives.
A
fractional
multistep
transformation
is
employed
to
convert
into
nonlinear
forms
respect
an
independent
variable.
After
performing
algebraic
manipulation,
are
trigonometric
hyperbolic
functions.
Our
analysis
demonstrates
that
wave
behavior
influenced
by
fractional-order
proposed
equations,
thus
providing
deeper
insights
composition
as
order
either
increases
or
decreases.
Additionally,
we
explore
effect
white
on
propagation
waves
solutions.
This
underscores
computational
robustness
adaptability
approach
investigate
phenomena
physical
sciences
engineering.</p>
Open Physics,
Journal Year:
2025,
Volume and Issue:
23(1)
Published: Jan. 1, 2025
Abstract
This
work
investigates
the
quadratic
and
quartic
nonlinear
diffusion–reaction
equations
with
convective
flux
terms,
which
are
investigated
analytically.
Diffusion–reaction
have
a
wide
range
of
applications
in
several
scientific
areas,
such
as
chemistry,
biology,
population
dynamics
species.
The
new
extended
direct
algebraic
method
is
applied
to
obtain
abundant
families
solitary
wave
solutions.
Different
types
solutions
obtained
by
applying
this
analytical
method.
approach
provides
form
single
combined
structures,
observed
shock,
complex
solitary-shock,
shock-singular,
periodic-singular
forms.
Some
depicted
graphically
illustrate
fact
that
they
are,
indeed,
mathematical
model.
Physica Scripta,
Journal Year:
2024,
Volume and Issue:
99(8), P. 085260 - 085260
Published: July 25, 2024
Abstract
In
this
study,
an
efficient
numerical
method
is
applied
to
KdV-Burger-Fisher
equation
which
one
of
the
dispersion-dissipation–reaction
model.
The
present
based
on
collocation
whose
weight
functions
are
taken
from
family
Dirac
delta
in
finite
element
methods.
selected
as
quintic
trigonometric
B-spline
basis.
error
norms
L
2
and
∞
calculated
measure
efficiency
method.
Numerical
solutions
obtained
via
basis
presented
tables
simulations
exhibited
well.
Additionally,
stability
analysis
investigated.
