On the solutions of coupled nonlinear time-fractional diffusion-reaction system with time delays

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Priyendhu, K. S., Prakash, P., Lakshmanan, M.
Format:	Preprint
Published:	2024
Subjects:	Analysis of PDEs Exactly Solvable and Integrable Systems 26A33, 33E12, 35Gxx, 35Kxx
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Nonlinear two-component system of time-fractional PDEs in (2+1)-dimensions: Invariant subspace method combined with variable transformation
by: Prakash, P., et al.
Published: (2024)

Suleimanov-Talanov self-focusing and the hierarchy of the focusing nonlinear Schrödinger equation
by: Buckingham, Robert J., et al.
Published: (2025)

The direct linearization scheme with the Lamé function: The KP equation and reductions
by: Li, Xing, et al.
Published: (2025)

Methods for exact solutions of nonlinear ordinary differential equations\
by: Conte, Robert, et al.
Published: (2025)

Inverse problem for a multi-term time-fractional diffusion equation with the Caputo derivatives
by: Ashurov, Ravshan, et al.
Published: (2026)

Painlevé Universality classes for the maximal amplitude solution of the Focusing Nonlinear Schrödinger Equation with randomness
by: Gkogkou, Aikaterini, et al.
Published: (2026)

Stability of KdV solitons
by: Wu, Derchyi
Published: (2024)

Large-time asymptotics for the defocusing Manakov system on nonzero background
by: Geng, Xianguo, et al.
Published: (2025)

Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems
by: Shepelsky, Dmitry, et al.
Published: (2023)

Nonlinear wave solution to a coupled mKdV equations with variable coefficients
by: Wu, Wenjuan
Published: (2025)

Principle of structural analogy of solutions and its application to nonlinear PDEs and delay PDEs
by: Polyanin, Andrei D.
Published: (2024)

Exact solutions and reductions of nonlinear Schrödinger equations with delay
by: Polyanin, Andrei D., et al.
Published: (2024)

Long time asymptotics for the KPII equation
by: Wu, Derchyi
Published: (2025)

Lie symmetry classification and group invariant solutions of generalized radial heat equation with nonlinear reaction source
by: Singh, Manjit, et al.
Published: (2026)

Spaces of initial conditions for quartic Hamiltonian systems of Painlevé and quasi-Painlevé type
by: Dell'Atti, Marta, et al.
Published: (2024)

An integrable pseudospherical equation with pseudo-peakon solutions
by: da Silva, Priscila Leal, et al.
Published: (2024)

Long-time asymptotics of the Sawada-Kotera equation on the line
by: Wang, Deng-Shan, et al.
Published: (2025)

Symmetries and exact solutions of a reaction-diffusion system arising in population dynamics
by: Broadbridge, Philip, et al.
Published: (2024)

Long-time asymptotic behavior of a mixed schrödinger equation with weighted Sobolev initial data
by: Cheng, Qiaoyuan, et al.
Published: (2020)

On $q$-Painlevé VI and the geometry of Segre surfaces
by: Roffelsen, Pieter
Published: (2023)

A $\mathcal C^\infty$-structure-based approach to traveling wave solutions of the gKdV equation
by: Pan-Collantes, Antonio J.
Published: (2025)

Spectral theory for self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the defocusing nonlinear Schroedinger equation with periodic boundary conditions
by: Biondini, Gino, et al.
Published: (2023)

On existence and properties of roots of third Painlevé' transcendents
by: Tertychniy, S. I.
Published: (2024)

On the Kaup-Broer-Kupershmidt systems
by: Klein, C., et al.
Published: (2024)

Spectral and linear stability of peakons in the Novikov equation
by: Lafortune, Stéphane
Published: (2023)

Parameter-free higher-order Schrodinger systems with weak dissipation and forcing
by: Keeler, Jack, et al.
Published: (2024)

Spectral instability of peakons for the $b$-family of Novikov equations
by: Deng, Xijun, et al.
Published: (2024)

Closed-form solutions of the nonlinear Schrödinger equation with arbitrary dispersion and potential
by: Polyanin, Andrei D., et al.
Published: (2024)

Eikonal 3.1: General solution for coupled system of eikonal equations, three space dimensions
by: Yehorchenko, Iryna
Published: (2024)

Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity
by: Deng, Xijun, et al.
Published: (2025)

The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach
by: de Monvel, Anne Boutet, et al.
Published: (2025)

Stability of Kadomtsev-Petviashvili multi-line solitons
by: Wu, Derchyi
Published: (2022)

The inverse scattering theory of Kadomtsev-Petviashvili II equations
by: Wu, Derchyi
Published: (2024)

Two-dimensional nonlinear Schrödinger equations with potential and dispersion given by arbitrary functions: Reductions and exact solutions
by: Polyanin, Andrei D.
Published: (2025)

Hybrid Ermakov-Ray-Reid/Painlevé II Symmetry Reduction: Application to a Class of Moving Boundary Problems
by: Rogers, Colin, et al.
Published: (2026)

Nonlocal conservation laws for the two-dimensional Euler equation in vorticity form
by: Morozov, Oleg I.
Published: (2025)

Conservation laws for a generalized seventh order KdV equation
by: Bruzón, María de los Santos, et al.
Published: (2024)

Generalized Navier-Stokes equations, associated with the Dolbeault complex
by: Alexander, Shlapunov, et al.
Published: (2025)

Rational Solutions of Painlevé V from Hankel Determinants and the Asymptotics of Their Pole Locations
by: Balogoun, Malik, et al.
Published: (2024)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"74cbe74f4ffa95a2e096cd3c146b3f49"
language	"en"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790867548.2771 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "74cbe74f4ffa95a2e096cd3c146b3f49" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"VUFIND_SESSION=74cbe74f4ffa95a2e096cd3c146b3f49; language=en; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"58543"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2406_10008/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2406_10008/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790867548.2621
REQUEST_TIME	1790867548

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"74cbe74f4ffa95a2e096cd3c146b3f49"
language	"en"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790867548.2771 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "74cbe74f4ffa95a2e096cd3c146b3f49" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"VUFIND_SESSION=74cbe74f4ffa95a2e096cd3c146b3f49; language=en; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"58543"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2406_10008/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2406_10008/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790867548.2621
REQUEST_TIME	1790867548

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: