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Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 12/2017, Volume 68, Issue 6, pp. 1 - 19
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic... 
Standing waves | Engineering | 35J20 | Mathematical Methods in Physics | Nonlinear Helmholtz equations | Oscillating solutions | 35Q55 | 35J05 | Theoretical and Applied Mechanics | EXISTENCE | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | BOUNDED SOLUTIONS | Mathematics - Analysis of PDEs
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 08/2017, Volume 343, p. 1
A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr... 
Helmholtz equations | Broken symmetry | Propagation | Boundary conditions | Optical bistability | Circular cylinders | Polarized light | Spectral methods | Bistability | Robustness (mathematics) | Nonlinearity | Iterative methods | Nonlinear systems | Cylinders
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 04/2019, Volume 346, pp. 260 - 287
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 10, pp. 3894 - 3901
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 6/2019, Volume 368, Issue 2, pp. 799 - 842
We prove an L p -version of the limiting absorption principle for a class of periodic elliptic differential operators of second order. The result is applied to... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | PHYSICS, MATHEMATICAL
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 09/2018, Volume 61, pp. 593 - 603
•A new method to obtain approximate fully analytical steady state solutions of NLODEs is presented.•The method is applied to the forced and damped... 
Nonlinear dynamics | Fourier series | Harmonic balance method | Helmholtz–Duffing equation | Anharmonic oscillator | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | RESONATORS | SYSTEMS | Helmholtz-Duffing equation | HARMONIC-BALANCE | Differential equations
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 05/2016, Volume 50, Issue 3, pp. 783 - 808
Journal Article
ADVANCED NONLINEAR STUDIES, ISSN 1536-1365, 08/2019, Volume 19, Issue 3, pp. 569 - 593
We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions... 
MATHEMATICS | MATHEMATICS, APPLIED | Nonlinear Helmholtz Equations | HARMONIC MAXWELL EQUATIONS | Curl-Curl Equations | Herglotz Waves | ABSENCE | Limiting Absorption Principles | OPERATORS | GROUND-STATES
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 03/2017, Volume 152, pp. 88 - 101
In the first part of this paper, the existence of infinitely many Lp-standing wave solutions for the nonlinear Helmholtz equation −Δu−λu=Q(x)∣u∣p−2u  in  RN is... 
Nonlinear Helmholtz equation | Pseudo-gradient flow | Variational method | SCHRODINGER-EQUATIONS | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | SEMILINEAR ELLIPTIC-EQUATIONS | INDEFINITE LINEAR PART | MULTIBUMP SOLUTIONS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2015, Volume 280, pp. 690 - 728
We set up a dual variational framework to detect real standing wave solutions of the nonlinear Helmholtz equation−Δu−k2u=Q(x)|u|p−2u,u∈W2,p(RN) with N≥3,... 
Standing waves | Nonlinear Helmholtz equation | Dual variational method | Nonvanishing | EXISTENCE | MATHEMATICS | SCALAR FIELD-EQUATIONS | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | OPERATORS | Mathematics - Analysis of PDEs
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, pp. 1 - 32
Abstract Using a dual variational approach, we obtain nontrivial real-valued solutions of the critical nonlinear Helmholtz equation $$-\Delta u-k^2u = Q(x)... 
nonvanishing | dual variational method | nonexistence results | Nonlinear Helmholtz equation | critical exponent
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 08/2018, Volume 331, pp. 457 - 472
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 12/2012, Volume 25, Issue 12, pp. 2349 - 2353
In this paper, we derive a class of analytical solution of the damped Helmholtz–Duffing oscillator that is based on a recently developed exact solution for the... 
Damped Helmholtz–Duffing oscillator | Mixed-parity nonlinear oscillator | Asymmetric behavior | Quadratic nonlinearities | Damped Helmholtz-Duffing oscillator | MATHEMATICS, APPLIED | INTEGRABILITY | OSCILLATOR | Mathematical analysis | Oscillators | Exact solutions
Journal Article
International Journal of Nonlinear Sciences and Numerical Simulation, ISSN 1565-1339, 2006, Volume 7, Issue 3, pp. 321 - 328
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 3, pp. 1338 - 1359
The well-posedness of a nonlinear Helmholtz equation with an impedance boundary condition is established for high frequencies in two and three dimensions.... 
Finite element method | Error estimates | Stability | Nonlinear Helmholtz equation | High wave number | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | high wave number | BOUNDARY-CONDITIONS | PREASYMPTOTIC ERROR ANALYSIS | DISCRETIZATIONS | NUMERICAL-SOLUTION | finite element method | PENALTY | nonlinear Helmholtz equation | POLLUTION | CIP-FEM | error estimates | stability
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 10/2016, Volume 39, pp. 134 - 148
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 06/2019, Volume 29, Issue 6, p. 063121
We study the formation and propagation of chirped elliptic and solitary waves in the cubic-quintic nonlinear Helmholtz equation. This system describes... 
OPTICAL PULSES | MATHEMATICS, APPLIED | TRANSMISSION | STABILITY | MEDIA | DISPERSIVE DIELECTRIC FIBERS | SPATIAL SOLITONS | PHYSICS, MATHEMATICAL | GLASSES | Physics - Pattern Formation and Solitons
Journal Article
Journal of Sound and Vibration, ISSN 0022-460X, 10/2013, Volume 332, Issue 21, pp. 5508 - 5522
In this paper, a novel description of periodic solution and homoclinic orbit of undamped Helmholtz—Duffing oscillator is proposed via nonlinear time... 
ACOUSTICS | QUADRATIC NONLINEAR OSCILLATORS | PERIODIC-SOLUTIONS | MECHANICS | LINDSTEDT-POINCARE METHOD | EQUATION | ENGINEERING, MECHANICAL
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 04/2019, Volume 60, Issue 4, p. 43508
We show that the Helmholtz equation describing the propagation of transverse electric waves in a Kerr slab with a complex linear permittivity εl and a complex... 
PHYSICS, MATHEMATICAL | Helmholtz equations | Wave propagation | Defocusing | Electromagnetic radiation | Permittivity | Slabs | Continuity (mathematics)
Journal Article
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