On certain new exact solutions of a diffusive predator-prey system
, 2012 We construct exact solutions for a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the $\big(\frac{G'}{G}\
Kraenkel, R. A. +2 more
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Auxiliary SDEs for homogenization of quasilinear PDEs with periodic coefficients
, 2004 We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term.
François Delarue, No. B
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AIMS MathematicsIn this article, we use the modified extended direct algebraic method (mEDAM) to explore and analyze the traveling wave phenomena embedded in the quintic conformable Benney-Lin equation (CBLE) that regulates liquid film dynamics.
Noorah Mshary
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Decay estimate of viscosity solutions of nonlinear parabolic PDEs and applications
Le Matematiche, 2014 The aim of this paper is to establish a decay estimate for viscosity solutions of nonlinear PDEs. As an application we prove existence and uniqueness for time almost periodic viscosity solutions.
Silvana Marchi
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Solving parametric PDE problems with artificial neural networks
, 2017 The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients.
Khoo, Yuehaw, Lu, Jianfeng, Ying, Lexing
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Periodic solutions to a mean-field model for electrocortical activity
, 2014 We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling
Green, Kevin, van Veen, Lennaert
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Asymptotic stability of breathers in some Hamiltonian networks of weakly coupled oscillators
, 2012 We consider a Hamiltonian chain of weakly coupled anharmonic oscillators. It is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space (breathers).
A. Giorgilli +33 more
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Singularites in the Bousseneq equation and in the generalized KdV equation
, 2001 In this paper, two kinds of the exact singular solutions are obtained by the improved homogeneous balance (HB) method and a nonlinear transformation. The two exact solutions show that special singular wave patterns exists in the classical model of some ...
A. C. Newell +31 more
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The Perturbed Chen–Lee–Liu Equation: Diverse Optical Soliton Solutions and Other Wave Solutions
Advances in Mathematical PhysicsThe objective of the present study is to extract the optical soliton solutions (OSSs) of the perturbed Chen–Lee–Liu equation by exerting three techniques, which are the extended Wang’s direct mapping method, tanh/coth function method and the Subequation ...
Kang-Jia Wang
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Computer assisted proof of branches of stationary and periodic solution, and Hopf bifurcations, for dissipative PDEs [PDF]
, 2021 Gianni Arioli
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