Journal of Computational and Nonlinear Dynamics,
Journal Year:
2024,
Volume and Issue:
19(10)
Published: July 20, 2024
Abstract
Prey
and
predator
are
the
important
factor
of
ecosystem.
Generally,
it
is
considered
that
prey–predator
models
depends
on
time
only
required
nonlinear
system
equations
for
its
dynamical
study.
But,
observed
such
species
can
move
from
one
to
place
another
in
a
way
there
need
which
also
spatial
as
well.
The
stochastic
investigated
numerically
analytically.
proposed
NSFD
used
numerical
study;
consistent
with
given
linear
stability
analysis
showed
unconditionally
stable.
There
two
equilibria
free
second
coexistence
equilibrium.
These
successfully
gained
case.
Extended
generalized
Riccati
equation
mapping
method
applied
analytical
obtained
solutions
form
rational,
hyperbolic,
trigonometric.
For
comparative
study,
unique
physical
problems
developed
their
simulations
drawn
various
choices
parameters.
graphical
behavior
depicts
efficacy
our
PLoS ONE,
Journal Year:
2025,
Volume and Issue:
20(1), P. e0306734 - e0306734
Published: Jan. 8, 2025
The
(3+1)-dimensional
mKdV
−
ZK
model
is
an
important
framework
for
studying
the
dynamic
behavior
of
waves
in
mathematical
physics.
goal
this
study
to
look
into
more
generic
travelling
wave
solutions
(TWSs)
generalized
ion-acoustic
scenario
three
dimensions.
These
exhibit
a
combination
rational,
trigonometric,
hyperbolic,
and
exponential
that
are
concurrently
generated
by
new
auxiliary
equation
unified
techniques.
We
created
numerous
soliton
solutions,
including
kink-shaped
anti-kink-shaped
bell-shaped
periodic
solitary
various
values
free
parameters
produced
solutions.
attained
displayed
geometrically
surface
plot
(3-D),
contour,
combined
two-dimensional
(2-D)
figures.
2-D
figure
would
make
it
easier
understand
impact
speed
wave.
Based
on
time,
influence
nonlinear
parameter
β
type
comprehensively
investigated
using
figures,
demonstrating
significant
nonlinearity.
graphical
representations
based
specific
settings,
which
help
grasp
model’s
intricate
general
behavior.
However,
results
research
compared
with
outcomes
obtained
published
literature
executed
other
scholars.
indicate
approach’s
effectiveness
reliability,
making
suitable
widespread
use
range
sophisticated
models.
techniques
successfully
generate
inventive
models,
crucial
Mathematics,
Journal Year:
2024,
Volume and Issue:
12(14), P. 2257 - 2257
Published: July 19, 2024
The
study
consists
of
the
distinct
types
exact
soliton
solutions
to
an
important
model
called
beta-time
fractional
(1
+
1)-dimensional
non-linear
Van
der
Waals
equation.
This
is
used
explain
motion
molecules
and
materials.
equation
explains
phase
separation
phenomenon.
Noncovalent
or
dispersion
forces
usually
have
effect
on
structure,
dynamics,
stability,
function
materials
in
different
branches
science,
including
biology,
chemistry,
physics.
Solutions
are
obtained,
dark,
dark-singular,
periodic
wave,
singular
many
more
wave
by
using
modified
extended
tanh
method.
Using
derivatives
makes
from
existing
solutions.
gained
results
will
be
high
importance
interaction
quantum-mechanical
fluctuations,
granular
matters,
other
applications
may
useful
fields
science
civil
engineering,
as
well
some
basic
physical
ones
like
those
studied
geophysics.
verified
represented
two-dimensional,
three-dimensional,
contour
graphs
Mathematica
software.
obtained
newer
than
results.
Stability
analysis
also
performed
check
stability
concerned
model.
Furthermore,
modulation
instability
stationary
helpful
future
studies
system.
In
end,
we
can
say
that
method
straightforward
dynamic,
it
a
tool
for
debating
tough
issues
wide
range
fields.
Open Physics,
Journal Year:
2024,
Volume and Issue:
22(1)
Published: Jan. 1, 2024
Abstract
This
investigation
explores
the
analytical
solutions
to
time-fractional
multi-dimensional
Navier–Stokes
(NS)
problem
using
advanced
approaches,
namely
Aboodh
residual
power
series
method
and
transform
iteration
method,
within
context
of
Caputo
operator.
The
NS
equation
governs
motion
fluid
flow
is
essential
in
dynamics,
engineering,
atmospheric
sciences.
Given
equation’s
extensive
diverse
applicability
across
several
disciplines,
we
are
motivated
conduct
a
thorough
analysis
understand
complex
dynamics
associated
with
nonlinear
events
it
describes.
For
this
purpose,
effectively
handle
challenges
posed
by
fractional
derivatives
utilizing
approach.
will
enable
us
obtain
accurate
approximations
for
time
equation.
By
conducting
computational
simulations,
provide
evidence
efficiency
dependability
suggested
methodologies
accurately
representing
dynamic
behavior
systems.
work
enhances
our
comprehension
utilization
calculus
provides
valuable
instruments
examining
intricate
phenomena.
Its
interdisciplinary
nature
ensures
that
findings
applicable
various
scientific
engineering
fields,
making
research
highly
versatile
impactful.
RSC Advances,
Journal Year:
2024,
Volume and Issue:
14(44), P. 32482 - 32500
Published: Jan. 1, 2024
Modern
technological
breakthroughs
depend
on
nonlinear
optical
(NLO)
and
photovoltaic
(PV)
materials,
essential
for
creating
advanced
photonic
devices
efficient
solar
cells.
