A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques called strategies. In this paper, we consider the problem of generating such Sudoku instances. We introdu...
Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology...
In this article, an analytical technique based on unified method is applied to investigate the exact solutions of non-linear homogeneous evolution partial differential equations. These partial differential equations are reduced to ordinary differenti...
In this article, we prove that the
In this paper, we consider the fractional Schrödinger–Hirota (FSH) equation in the sense of a conformable fractional derivative. Through a traveling wave transformation, we change the FSH equation to an ordinary differential equation. We o...
In this paper, we consider how to find new exact solutions for nonlinear partial differential equations using the extended Kudryashov method. This method mainly uses the Riccati equation and the Bernoulli equation where there are some underdetermined...
In this paper, the exp-function method is improved to construct exact solutions of non-linear lattice equations by modifying its exponential function ansätz. The improved method has two advantages. One is that it can solve non-linear lattice equation...
In this paper, a space-time finite element method based on a Galerkin-weighted residual method is proposed to solve the nonlinear fully intrinsic equations of geometrically exact beam which are first-order partial differential equations about time an...
The current manuscript investigates the exact solutions of the modified Benjamin-Bona-Mahony (BBM) equation. Due to its efficiency and simplicity, the modified auxiliary equation method is adopted to solve the problem under consideration. As a result...
The objective of this present paper is to utilize an auxiliary equation method for constructing exact solutions associated with variable coefficient function forms for certain nonlinear partial differential equations (NPDEs) in the sense of the confo...
We present a short review of the methodology and applications of the Simple Equations Method (SEsM) for obtaining exact solutions to nonlinear differential equations. The applications part of the review is focused on the simple equations used, with e...
A number of solitary wave solutions for microtubules (MTs) are observed in this article by using the modified exp-function approach. We tackle the problem by treating the results as nonlinear RLC transmission lines, and then finding exact solutions t...
In this paper, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation forced by multiplicative noise. To obtain the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation, we apply the
We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities. We present an amended version of the methodology, which is based on the use of composite...
This paper systematically studies the exact analytical solutions of the (2+1)-dimensional generalized Burgers–Fisher (gBF) equation. Using the Lie symmetry analysis method, the infinitesimal generators of the equation are derived. Through symme...
The delay differential equations are of great importance in real-life phenomena. A special type of these equations is the Pantograph delay differential equation. Generally, solving a delay differential equation is a challenge, especially when the com...
A new class of truncated M-fractional exact soliton solutions for a mathematical physics model known as a truncated M-fractional (1+1)-dimensional nonlinear modified mixed-KdV model are achieved. We obtain these solutions by using a modified extended...
This study explores the (1+1)-dimensional Klein–Fock–Gordon equation, a distinct third-order nonlinear differential equation of significant theoretical interest. The Klein–Fock–Gordon equation (KFGE) plays a pivotal role in th...
In this paper, a differential quadrature method of high-order precision (DQ−Pade), which is equivalent to the generalized Pade approximation for approximating the end of a time or spatial interval, is used to solve nonlinear fully intrinsic equ...
We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independe...
In this paper, we use the modified exp
The paper shows that, in looking for exact solutions to nonlinear PDEs, the direct method of functional separation of variables can, in certain cases, be more effective than the method of differential constraints based on the compatibility analysis o...
Nowadays, portrait drawing has become increasingly popular as a means of developing artistic skills and nurturing emotional expression. However, it is challenging for novices to start learning it, as they usually lack a solid grasp of proportions and...
Bilevel optimization is a fundamental framework for hierarchical decision-making, but its solution is challenging due to the implicit and typically set-valued nature of the lower-level optimality condition. In this paper, we study bilevel optimizatio...
Eigenvector sensitivities are often used in many engineering problems such as structural vibration control, optimization design, model updating and damage identification. So far, modal superposition method and Nelson’s method are the two main m...
The paper consists of various types of wave solutions for the truncated M-fractional Bateman–Burgers equation, a significant mathematical physics equation. This model describes the nonlinear waves and solitons in different physical fields such...
Penalty function methods are fundamental for solving constrained optimization problems, yet the widely used
In clinical studies focusing on paired body parts, diseases can manifest on either both sides (bilateral) or just one side (unilateral) of the organs. Consequently, the data in these studies may consist of records from both bilateral and unilateral c...
In this paper, we investigate high-order soliton solutions of the Kundu–Eckhaus equation using the Dbar method. As a key technique in the field of integrable systems, the Dbar method occupies an important position in the study of exact solution...
In this paper, we propose an exact model-based method for near-field sources localization with a bistatic multiple input, multiple output (MIMO) radar system, and compare it with an approximated model-based method. The aim of this paper is to propose...
Calculating the large deflection of a cantilever beam is one of the common problems in engineering. The differential equation of a beam under large deformation, or the typical elastica problem, is hard to approximate and solve with the known solution...
The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglectin...
To realize the measurement and exact reconstruction of a pair of parallel profiles, a new scanning method using four displacement sensors as probes and different probe spacings has been invented with the advantage of preventing data processing error....
Inhomogeneous random graphs are commonly used models for complex networks where nodes have varying degrees of connectivity. Computing the degree distribution of such networks is a fundamental problem and has important applications in various fields....
We develop the binary-shadow method for exact CNOT counting and apply it to arbitrary wire permutations. The Heisenberg evolution of rotated local Z observables converts every CNOT gate into an elementary transvection over
This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering...
The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear opt...
In this article, the exact solutions of the stochastic conformable Broer–Kaup equations with conformable derivatives which describe the bidirectional propagation of long waves in shallow water are obtained using the modified exponential functio...
As a key technology for the fifth-generation of mobile communications, massive MIMO systems enable massive user access via large-scale arrays. However, their dense deployment extends the near-field (NF) region, introducing new localization complexiti...
The Laplace residual power series method was introduced as an effective technique for finding exact and approximate series solutions to various kinds of differential equations. In this context, we utilize the Laplace residual power series method to g...
There has been considerable interest in seeking exact solutions of non-linear evolution equations that describe important physical and biological processes. Nonetheless, it is a difficult undertaking to determine closed form solutions of mathematical...
High penetration of distributed photovoltaics (PV) makes hosting-capacity assessment and active distribution network operation challenging, primarily due to the need to accurately restore nonconvex branch-flow equalities rather than relying on relaxa...
We study a fifth order time-fractional KdV equation (FKdV) under meaning of the conformal fractional derivative. By trial equation method based on symmetry, we construct the abundant exact traveling wave solutions to the FKdV equation. These solution...
We studied obtaining exact solutions to a set of equations related to the SEIR (Susceptible-Exposed-Infectious-Recovered) model of epidemic spread. These solutions may be used to model epidemic waves. We transformed the SEIR model into a differential...
The paper describes essential reaction–diffusion models with delay arising in population theory, medicine, epidemiology, biology, chemistry, control theory, and the mathematical theory of artificial neural networks. A review of publications on...
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematic...
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connec...
This manuscript focuses attention on new exact solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The extended trial equation method (ETEM), w...
Gwet’s first-order agreement coefficient (AC
In this paper, the
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