Globally integrable quantum systems and their perturbations

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Bambusi, Dario, Langella, Beatrice
Format:	Preprint
Published:	2024
Subjects:	Analysis of PDEs 37K10, 35Q55
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Non relativistic limit of the nonlinear Klein-Gordon equation: Uniform in time approximation of KAM solutions
by: Bambusi, Dario, et al.
Published: (2025)

Global-in-time Well-posedness of the One-dimensional Hydrodynamic Gross-Pitaevskii Equations without Vacuum
by: Wegner, Robert
Published: (2023)

Global well-posedness of the NLS hierarchy with nonzero boundary condition
by: Liao, Xian, et al.
Published: (2025)

Intermediate long wave equation in negative Sobolev spaces
by: Chapouto, Andreia, et al.
Published: (2023)

On the global well-posedness of the Calogero-Sutherland derivative nonlinear Schrödinger equation
by: Badreddine, Rana
Published: (2023)

Traveling waves & finite gap potentials for the Calogero-Sutherland Derivative nonlinear Schrödinger equation
by: Badreddine, Rana
Published: (2023)

On the well-posedness of the intermediate nonlinear Schrödinger equation on the line
by: Chapouto, Andreia, et al.
Published: (2025)

Turbulent Threshold for Continuum Calogero-Moser Models
by: Hogan, James, et al.
Published: (2024)

Shallow-water convergence of the intermediate long wave equation in $L^2$
by: Chapouto, Andreia, et al.
Published: (2025)

Soliton resolution for Calogero--Moser derivative nonlinear Schrödinger equation
by: Kim, Taegyu, et al.
Published: (2024)

Construction of smooth chiral finite-time blow-up solutions to Calogero--Moser derivative nonlinear Schrödinger equation
by: Kim, Kihyun, et al.
Published: (2024)

Quantized blow-up dynamics for Calogero--Moser derivative nonlinear Schrödinger equation
by: Jeong, Uihyeon, et al.
Published: (2024)

Classification of single-bubble blow-up solutions for Calogero--Moser derivative nonlinear Schrödinger equation
by: Jeong, Uihyeon, et al.
Published: (2026)

Estimates for the Gross-Pitaevskii equation linearized around a vortex
by: Collot, Charles, et al.
Published: (2025)

A Unified Integral Equation Approach to Conservation Laws for Nonlinear Schrödinger Equations
by: Machihara, Shuji, et al.
Published: (2026)

The uniqueness of the ground state and the dynamics of nonlinear Schrödinger equation with inverse square potential
by: Yang, Kai, et al.
Published: (2026)

Gibbs dynamics for fractional nonlinear Schrödinger equations with weak dispersion
by: Liang, Rui, et al.
Published: (2023)

Scattering for the dispersion managed nonlinear Schrödinger equation
by: Choi, Mi-Ran, et al.
Published: (2024)

The modified Camassa-Holm equation on the half line: a Riemann--Hilbert approach
by: Karpenko, Iryna, et al.
Published: (2025)

General rogue waves of infinite order: Exact properties, asymptotic behavior, and effective numerical computation
by: Bilman, Deniz, et al.
Published: (2024)

The nonlinear Schrödinger equation on the half-space
by: Himonas, A. Alexandrou, et al.
Published: (2024)

Asymptotic stability of smooth solitons and multi-solitons for the Camassa--Holm equation
by: Chen, Robin Ming, et al.
Published: (2026)

NLS approximation for a scalar FPUT system on a 2D square lattice with a cubic nonlinearity
by: Giannoulis, Ioannis, et al.
Published: (2024)

Global well-posedness for the defocusing cubic nonlinear Schrödinger equation on $\Bbb T^3$
by: Song, Yilin, et al.
Published: (2024)

Global well-posedness, scattering and blow-up for the energy-critical, Schrödinger equation with indefinite potential in the radial case
by: Wang, Jun, et al.
Published: (2024)

Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori
by: Bernier, Joackim, et al.
Published: (2024)

Blow-up dynamics for radial self-dual Chern-Simons-Schrödinger equation with prescribed asymptotic profile
by: Kim, Kihyun, et al.
Published: (2024)

Soliton resolution for equivariant self-dual Chern-Simons-Schrödinger equation in weighted Sobolev class
by: Kim, Kihyun, et al.
Published: (2022)

Remarks on the derivation of the virial identity for nonlinear Schrödinger equations
by: Ikeda, Tomoyuki, et al.
Published: (2025)

An Explicit Formula for the Benjamin-Ono Hierarchy with Applications to Traveling Waves and Zero-Dispersion Limits
by: Gérard, Patrick, et al.
Published: (2026)

Wellposedness for the KdV hierarchy
by: Klaus, Friedrich, et al.
Published: (2023)

A remark on the well-posedness of the modified KdV equation in $L^2$
by: Forlano, Justin
Published: (2022)

Ill-posedness in the critical Sobolev space for the $b$-Novikov equation
by: Geba, Dan-Andrei, et al.
Published: (2026)

Global higher integrability for systems with $p$-growth structure in noncylindrical domains
by: Moring, Kristian, et al.
Published: (2025)

On the convergence of explicit formulas for $L^2$ solutions to the Benjamin-Ono and continuum Calogero-Moser equations
by: Bronsard, Yvonne Alama, et al.
Published: (2026)

Lipschitz Stability for an Inverse Problem of Biharmonic Wave Equations with Damping
by: Bi, Minghui, et al.
Published: (2026)

On the dispersive estimates for the discrete Schrödinger equation on a honeycomb lattice
by: Hong, Younghun, et al.
Published: (2025)

Nekhoroshev type stability for non-local semilinear Schrödinger equations
by: Yu, Bingqi, et al.
Published: (2025)

Well-posedness of the Muskat problem in subcritical $L_p$-Sobolev spaces
by: Abels, Helmut, et al.
Published: (2020)

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	"94960370761add81c57cb721079b16d1"
language	"en"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1791233809.847 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "94960370761add81c57cb721079b16d1" ]`]
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=94960370761add81c57cb721079b16d1; 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	"216.73.216.28"
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	"10489"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2403_18670/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2403_18670/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1791233809.8416
REQUEST_TIME	1791233809

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"94960370761add81c57cb721079b16d1"
language	"en"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1791233809.847 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "94960370761add81c57cb721079b16d1" ]`]
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=94960370761add81c57cb721079b16d1; 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	"216.73.216.28"
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	"10489"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2403_18670/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2403_18670/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1791233809.8416
REQUEST_TIME	1791233809

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: