Ill-posedness for periodic nonlinear dispersive equations by Jaime Angulo Pava, Sevdzhan Hakkaev

“…In this article, we establish new results about the ill-posedness of the Cauchy problem for the modified Korteweg-de Vries and the defocusing modified Korteweg-de Vries equations, in the periodic case. The lack of local well-posedness is in the sense that the dependence of solutions upon initial data fails to be continuous. …”
Get full text

Exact solutions to the space–time fractional shallow water wave equation via the complete discrimination system for polynomial method by Nan Yang, Wenlong Xu, Kai Zhang, Bailin Zheng

“…The work of this article is to transform the famous nonlinear space–time fractional shallow water wave equations, namely coupled Korteweg-de Vries equations into ordinary differential equations via the complex fractional traveling wave transformation, and find the exact solutions through the complete discrimination system for polynomial method. …”
Get full text

KP governs random growth off a 1-dimensional substrate by Jeremy Quastel, Daniel Remenik

“…The Tracy–Widom distributions appear as special self-similar solutions of the KP and Korteweg–de Vries equations. In addition, it is noted that several known exact solutions of the KPZ equation also solve the KP equation.…”
Get full text

Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems by Wen-Xiu Ma

“…We focus on two expository examples: nonlocal PT-symmetric matrix nonlinear Schrödinger and modified Korteweg–de Vries equations.…”
Get full text

The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation by Hassan Khan, Hassan Khan, Qasim Khan, Fairouz Tchier, Gurpreet Singh, Poom Kumam, Poom Kumam, Ibrar Ullah, Kanokwan Sitthithakerngkiet, Ferdous Tawfiq

“…In the present article, an extension to this idea is presented to obtain the solutions of non-linear fractional Korteweg–de Vries equations. The solutions comparison of the proposed problems is done via two analytical procedures, which are known as the Residual power series method (RPSM) and q-HATM, respectively. …”
Get full text

Analog black-white hole solitons in traveling wave parametric amplifiers with superconducting nonlinear asymmetric inductive elements by Haruna Katayama, Noriyuki Hatakenaka, Toshiyuki Fujii, Miles P. Blencowe

“…The SNAIL-TWPA circuit dynamics are described by the Korteweg–de Vries or modified Korteweg–de Vries equations in the continuum field approximation, depending on the external magnetic flux bias, and validated numerically. …”
Get full text

New Travelling Wave Solution-Based New Riccati Equation for Solving KdV and Modified KdV Equations by Rezazadeh Hadi, Korkmaz Alper, EL Achab Abdelfattah, Adel Waleed, Bekir Ahmet

“…A large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. …”
Get full text

Electron acoustic counterpropagating multi-solitons and rogue waves collision in an unmagnetized plasma in the presence of critical density ratios by M. G. Hafez, Shahrina Akter, R. Sakthivel

“…Using the concept of Hirota’s bilinear method, the useful forms of multi-solitons solutions of the coupled modified Korteweg–de Vries equations (mKdVEs) are determined. Furthermore, the coupled nonlinear Schrödinger equations (NLSEs) are derived from mKdVEs using the appropriate starching coordinates. …”
Get full text

Solving Nonlinear Partial Differential Equations of Special Kinds of 3rd Order Using Balance Method and Its Models by Daba Meshesha Gusu, Wakjira Gudeta

“…Finally, the proposed method is a standard, effective, and easily computable method for solving the modified Korteweg–de Vries equations and determining its perspective models.…”
Get full text

Metastability of solitary waves in diatomic FPUT lattices by Nickolas Giardetti, Amy Shapiro, Stephen Windle, J. Douglas Wright

“…It is known that long waves in spatially periodic polymer Fermi-Pasta-Ulam-Tsingou lattices are well-approximated for long, but not infinite, times by suitably scaled solutions of Korteweg-de Vries equations. It is also known that dimer FPUT lattices possess nanopteron solutions, i.e., traveling wave solutions which are the superposition of a KdV-like solitary wave and a very small amplitude ripple. …”
Get full text

Non classical interaction aspects to a nonlinear physical model by Hajar F. Ismael, Usman Younas, Tukur Abdulkadir Sulaiman, Naila Nasreen, Nehad Ali Shah, Mohamed R. Ali

“…The (2+1)-dimensional NNV equations are the isotropic Lax integrable extension of the (1+1)-dimensional Korteweg–de Vries equations. Fractional differential models (FDMs) from the corresponding integer order model can describes more complex behavior and even cover all properties of integer order model. …”
Get full text