The Initial Value Problem for the Quadratic Nonlinear Klein-Gordon Equation by Nakao Hayashi, Pavel I. Naumkin

“…We study the initial value problem for the quadratic nonlinear Klein-Gordon equation ℒ𝑢=⟨𝑖𝜕𝑥⟩−1𝑢2, (𝑡,𝑥)∈𝐑×𝐑, 𝑢(0,𝑥)=𝑢0(𝑥), 𝑥∈𝐑, where ℒ=𝜕𝑡+𝑖⟨𝑖𝜕𝑥⟩ and ⟨𝑖𝜕𝑥⟩=1−𝜕2𝑥. …”
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Decay of solutions of a system of nonlinear Klein-Gordon equations by José Ferreira, Gustavo Perla Menzala

Subjects: “…nonlinear Klein-Gordon equations…”
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Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients by Nauman Raza, Asma Rashid Butt, Ahmad Javid

“…The nonlinear Klein-Gordon equation (KGE) models many nonlinear phenomena. …”
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Solutions of Three Dimensional Nonlinear Klein-Gordon Equations by Using Quadruple Laplace Transform by Wubshet Ibrahim, Mesele Tamiru

“…This study was designed in order to show the quadruple Laplace transform with an iterative method for solving three-dimensional nonlinear Klein-Gordon equations. The quadruple Laplace transform with the iterative method was aimed at getting analytical solutions of three-dimensional nonlinear Klein-Gordon equations. …”
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A conservative fully discrete finite element scheme for the nonlinear Klein–Gordon equation by R. Z. Dautov, G. R. Salimzyanova

“…This article proposes a family of the Petrov–Galerkin–FEM methods that can be used to solve the nonlinear Klein–Gordon equation. The discrete schemes were formulated based on the solution of the problem and its time derivative. …”
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Solutions of the nonlinear Klein-Gordon equation and the generalized uncertainty principle with the hybrid analytical and numerical method by Narges Heidari, Marc de Montigny, Ali Ahmadi Azar, Thambiayya Sathiyaraj, Hassan Hassanabadi

Subjects: “…Nonlinear Klein-Gordon equation…”
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Global Existence and Blow-Up of Solutions for Nonlinear Klein-Gordon Equation with Damping Term and Nonnegative Potentials by Wen-Yi Huang, Wen-Li Chen

“…This paper is concerned with the nonlinear Klein-Gordon equation with damping term and nonnegative potentials. …”
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Soliton stability and topological invariants in a generalized nonlinear Klein–Gordon equation: Existence, dynamics, and conservation laws by José Luis Díaz Palencia

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A Reliable Treatment of Homotopy Perturbation Method for Solving the Nonlinear Klein-Gordon Equation of Arbitrary (Fractional) Orders by A. M. A. El-Sayed, A. Elsaid, D. Hammad

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A new numerical technique for the solution of time-fractional nonlinear Klein–Gordon equation involving Atangana–Baleanu derivative using cubic B-spline functions by Shaheen Muserat, Abbas Muhammad, Abdullah Farah Aini, Hamed Yasser Salah

Subjects: “…time-fractional nonlinear klein–gordon equation…”
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Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns by Hadi Rezazadeh, Mohammad Ali Hosseinzadeh, Lahib Ibrahim Zaidan, Fatima SD. Awad, Fiza Batool, Soheil Salahshour

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Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics by Khaled A. Gepreel

“…We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. …”
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