Recently, Lin et al. (Appl. Math. Lett. 78 (2018) 112–117) established the resonant multiple-wave solution of a generalized Kadomtsev–Petviashvili (gKP) equation with applications in applied sciences ...using the linear superposition technique. In the present paper, according to the results obtained by Lin et al. and adopting a systematic method established by Zhou and Manukure, the positive multi-complexiton solution to the generalized Kadomtsev–Petviashvili equation is constructed for the first time. Several simulations in three dimensions are conducted formally in order to examine the dynamic behavior of positive multi-complexiton solutions, particularly the positive single-, double-, and triple-complexion waves. The current research outcomes definitely will enrich studies related to the gKP equation and its exact solutions.
Based on Jacobi polynomials, an operational method is proposed to solve the generalized Abel’s integral equations (a class of singular integral equations). These equations appear in various fields of ...science such as physics, astrophysics, solid mechanics, scattering theory, spectroscopy, stereology, elasticity theory, and plasma physics. To solve the Abel’s singular integral equations, a fast algorithm is used for simplifying the problem under study. The Laplace transform and Jacobi collocation methods are merged, and thus, a novel approach is presented. Some theorems are given and established to theoretically support the computational simplifications which reduce costs. Also, a new procedure for estimating the absolute error of the proposed method is introduced. In order to show the efficiency and accuracy of the proposed method some numerical results are provided. It is found that the proposed method has lesser computational size compared to other common methods, such as Adomian decomposition, Homotopy perturbation, Block-Pulse function, mid-point, trapezoidal quadrature, and product-integration. It is further found that the absolute errors are almost constant in the studied interval.
In recent years, numerical methods have been introduced to solve two-dimensional Volterra and Fredholm integral equations. In this study, a numerical scheme is constructed to solve classes of linear ...and nonlinear three-dimensional integral equations (Volterra, Fredholm, and mixed Volterra–Fredholm). This operational approach is proposed to easily and directly solve these equations at low computational costs. The scheme is based on the Jacobi polynomials on the interval 0, 1 where three-variable Jacobi polynomials are introduced and their operational matrices of integration and product are derived. Compared to other existing methods for multidimensional problems, the Jacobi operational method eliminates the time-consuming computations and solely employs the one-dimensional operational matrix to construct corresponding multidimensional operational matrices. The absolute error of the proposed method is almost constant on the studied interval even at higher dimensions, confirming the stability of the proposed operational Jacobi method. Required theorems on the convergence of the method are proved in Jacobi-weighted Sobolev space. It is established that the error function vanishes as N increases. The method is evaluated using several illustrative examples which indicate the proposed method with lesser computational size compared to the Block–Pulse functions, differential transform, and degenerate kernel methods.
Obsessive-compulsive personality disorder (OCPD) has been subject to numerous definition and classification changes, which has contributed to difficulties in reliable measurement of the disorder. ...Consequently, OCPD measures have yielded poor validity and inconsistent prevalence estimates. Reliable and valid measures of OCPD are needed. The aim of the current study was to examine the factor structure and psychometric properties of the Pathological Obsessive Compulsive Personality Scale (POPS). Participants (N = 571 undergraduates) completed a series of self-report measures online, including the POPS. Confirmatory factor analysis was used to compare the fit of unidimensional, five factor, and bifactor models of the POPS. Convergent and divergent validity were assessed in relation to other personality dimensions. A bifactor model provided the best fit to the data, indicating that the total POPS scale and four subscales can be scored to obtain reliable indicators of OCPD. The POPS was most strongly associated with a disorder-specific measure of OCPD, however there were also positive associations with theoretically disparate constructs, thus further research is needed to clarify validity of the scale.
The aim of the current paper is to construct the shifted fractional-order Jacobi functions (SFJFs) based on the Jacobi polynomials to numerically solve the fractional-order pantograph differential ...equations. To achieve this purpose, first the operational matrices of integration, product, and pantograph, related to the fractional-order basis, are derived (operational matrix of integration is derived in Riemann–Liouville fractional sense). Then, these matrices are utilized to reduce the main problem to a set of algebraic equations. Finally, the reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. Also, some theorems are presented on existence of solution of the problem under study and convergence of our method.
The present paper examines the dynamical features of solitary waves in a weakly nonlinear medium. More precisely, the propagation of solitary waves in a system is modeled by a fourth-order nonlinear ...Schrödinger equation involving diffraction, power law nonlinearity, and weak nonlocality. Several localized waves classified as bright and dark solitons to the governing model are derived using ansatz methods. It is shown how power and nonlocality coefficients affect the dynamics of bright and dark solitons. Furthermore, the modulational instability of continuous waves in the presence of such different effects is studied. The results of the current paper represent a significant advancement in exploring the propagation of solitary waves in a nonlinear medium.
The present paper intends to thoroughly study an evolutionary model called the Zakharov–Kuznetsov modified equal-width (ZK–MEW) equation. More precisely, Lie symmetries as well as invariant solutions ...to the ZK–MEW equation describing shallow and stratified waves in nonlinear LC circuits are first derived, and then a general theorem established by Ibragimov is adopted to retrieve its conservation laws. Additionally, by applying the qualitative theory of dynamical systems, the bifurcation analysis of the dynamical system is carried out and several Jacobi elliptic solutions to the ZK–MEW equation are formally constructed. In some case studies, the impact of the nonlinear coefficient on the physical features of bright and kink solitary waves as well as periodic continuous waves is examined in detail.
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