Skip to main content
SpringerLink
Log in

The Role of the Massless Phantom Term in the Stability of a Non-Topological Soliton Solution

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions A: Science Aims and scope Submit manuscript

Abstract

We intend to introduce classically a special Lagrangian density in such a way that, firstly, it leads to a special non-topological solitary wave solution, secondly, the stability of that is guaranteed properly, and thirdly, its dominant dynamical equations reduce to the standard nonlinear Klein–Gordon equations. For these purposes, we have to consider a new term in the Lagrangian density, whose role is like a massless phantom that surrounds the special solitary wave solution and resists any change in its internal structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anagnostopoulos KN, Axenides M et al (2001) Large gauged Q balls. Phys Rev D 64:125006

    Article  Google Scholar 

  • Axenides M, Komineas S et al (2000) Dynamics of nontopological solitons: Q balls. Phys Rev D 61:085006

    Article  Google Scholar 

  • Bazeia D, Losano L et al (2016) Compact Q-balls. Phys Lett B 758:146–151

    Article  MATH  Google Scholar 

  • Bazeia D, Losano L et al (2017) Split Q-balls. Phys Lett B 765:359

    Article  MathSciNet  MATH  Google Scholar 

  • Bazeia D, Marques MA, Menezes R (2016) Exact solutions, energy, and charge of stable Q-balls. Eur Phys J C 76:241

    Article  Google Scholar 

  • Bazeia D, Belendryasova E, Gani VA (2018) Scattering of kinks of the sinh-deformed \(\varphi ^4\) model. Eur Phys J C 78:340

    Article  Google Scholar 

  • Bowcock P, Foster D, Sutcliffe P (2009) Q-balls, integrability and duality. J Phys A Math Theor 42:085403

    Article  MathSciNet  MATH  Google Scholar 

  • Campbell DK, Peyrard M (1986) Kink-antikink interactions in the double sine-Gordon equation. Physica D 19:165

    Article  MathSciNet  Google Scholar 

  • Campbell DK, Peyrard M (1986) Solitary wave collisions revisited. Physica D 18:47

    Article  MathSciNet  MATH  Google Scholar 

  • Campbell DK, Schonfeld JS, Wingate CA (1983) Resonance structure in kink-antikink interactions in \(\phi ^4\) theory. Physica D 9:1

    Article  Google Scholar 

  • Charkina OV, Bogdan MM (2006) Internal modes of solitons and near-integrable highly-dispersive nonlinear systems. Symmetry Integr Geom 2:047

    MathSciNet  MATH  Google Scholar 

  • Coleman S (1985) Q-balls. Nucl Phys B 262:263

    Article  MathSciNet  Google Scholar 

  • Das A (1989) Integrable models. World Scientific, Singapore

    Book  MATH  Google Scholar 

  • Dorey P, Romańczukiewicz T (2018) Resonant kink-antikink scattering through quasinormal modes. Phys Lett B 779:117–123

    Article  Google Scholar 

  • Dorey P, Mersh K, Romanczukiewicz T, Shnir Y (2011) Kink-antikink collisions in the \(\varphi ^6\) model. Phys Rev Lett 107:091602

    Article  Google Scholar 

  • Drazin PG, Johnson RS (1989) Solitons: an Introduction. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • El-Nabulsi AR (2013) Non-linear dynamics with non-standard Lagrangians. Qual Theory Dyn Syst 12:273

    Article  MathSciNet  MATH  Google Scholar 

  • El-Nabulsi RA (2014) Nonlinear integro-differential Einstein’s field equations from nonstandard Lagrangians. Can J Phys 92:1149–1153

    Article  Google Scholar 

  • El-Nabulsi RA (2015) Classical string field mechanics with non-standard Lagrangians. Math Sci 9:173–179

    Article  MathSciNet  MATH  Google Scholar 

  • Gani VA, Kudryavtsev AE (1999) Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies. Phys Rev E 60:3305

    Article  Google Scholar 

  • Gani VA, Kudryavtsev AE, Lizunova MA (2014) Kink interactions in the \((1+1)\)-dimensional \(\varphi ^6\) model. Phys Rev D 89:125009

    Article  Google Scholar 

  • Gani VA, Lensky V, Lizunova MA (2015) Kink excitation spectra in the (1+1)-dimensional \(\varphi ^8\) model. JHEP 8:147

    Article  MathSciNet  MATH  Google Scholar 

  • Gani VA, Moradi Marjane A, Askari A et al (2018) Scattering of the double sine-Gordon kinks. Eur Phys J C 78:345

    Article  Google Scholar 

  • Gharaati AR, Riazi N, Mohebbi F (2006) Internal modes of relativistic solitons. Int J Theor Phys 45:53

    Article  MATH  Google Scholar 

  • Goodman RH, Haberman R (2005) Kink-antikink collisions in the \(\phi ^4\) equation: the n-bounce resonance and the separatrix map. SIAM J Appl Dyn Syst 4:1195

    Article  MathSciNet  MATH  Google Scholar 

  • Khare A, Christov IC, Saxena A (2014) Successive phase transitions and kink solutions in \(\phi ^8\), \(\phi ^{10}\) and \(\phi ^{12}\) field theories. Phys Rev E 90:023208

    Article  Google Scholar 

  • Kovtun A, Nugaev E, Shkerin A (2018) Vibrational modes of Q-balls. Phys Rev D 98:096016

    Article  MathSciNet  Google Scholar 

  • Lamb GL Jr (1980) Elements of soliton theory. Wiley, Hoboken

    MATH  Google Scholar 

  • Lee TD, Pang Y (1992) Nontopological solitons. Phys Rep 221:251

    Article  MathSciNet  Google Scholar 

  • Mahzoon MH, Riazi N (2007) Nonlinear electrodynamics and NED-inspired chiral solitons. Int J Theor Phys 46:823

    Article  MATH  Google Scholar 

  • Manton N, sutcliffe P (2004) Topological solitons. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Mohammadi M, Olamaei AR (2017) Soliton-like solutions of the complex non-linear Klein-Gordon systems in 1 + 1 dimensions. IJAA 4:57–68

    Google Scholar 

  • Mohammadi M, Riazi N (2011) Approaching integrality in bi-dimensional nonlinear field equations. Prog Theor Phys 126:237

    Article  MATH  Google Scholar 

  • Mohammadi M, Riazi N (2014) Bi-dimensional soliton-like solutions of the nonlinear complex sine-Gordon system. Prog Theor Exp Phys 2014:023A03

    Article  MATH  Google Scholar 

  • Mohammadi M, Riazi N (2019) The affective factors on the uncertainty in the collisions of the soliton solutions of the double field sine-Gordon system. Commun Nonlinear Sci Numer Simul 72:176–193

    Article  MathSciNet  Google Scholar 

  • Mohammadi M, Riazi N, Azizi A (2012) Radiative properties of kinks in the \(\sin ^4 (\phi )\) system. Prog Theor Phys 128:615

    Article  Google Scholar 

  • Moradi Marjaneh A, Gani VA, Saadatmand D (2017) Multi-kink collisions in the \(\phi ^6\) model. J High Energy Phys 2017:28

    Article  MathSciNet  MATH  Google Scholar 

  • Musielak ZE (2008) Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients. J Phys A Math Theor 41:055205

    Article  MathSciNet  MATH  Google Scholar 

  • Panin AG, Smolyakov MN (2017) Problem with classical stability of U(1) gauged Q-balls. Phys Rev D 95:065006

    Article  MathSciNet  Google Scholar 

  • Peyrard M, Campbell DK (1983) Kink antikink interactions in a modified sine-Gordon model. Physica D 9:33

    Article  Google Scholar 

  • Peyravi M, Montakhab A, Riazi N, Gharaati A (2009) Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation. Eur Phys J B 72:269

    Article  MATH  Google Scholar 

  • Polyakov AM (1974) Particle spectrum in quantum field theory. JETP Lett 20:430

    Google Scholar 

  • Popov CA (2005) Perturbation theory for the double sine-Gordon equation. Wave Motion 42:309

    Article  MathSciNet  MATH  Google Scholar 

  • Rajaraman R (1982) Solitons and instantons. Elsevier, Amsterdam

    MATH  Google Scholar 

  • Riazi N (2011) Wave-particle duality in nonlinear Klein-Gordon equation. Int J Theor Phys 50:3451

    Article  MathSciNet  MATH  Google Scholar 

  • Saha A, Talukdar B (2014) Inverse variational problem for nonstandard Lagrangians. Rep Math Phys 73:299–309

    Article  MathSciNet  MATH  Google Scholar 

  • Shiromizu T (1998) Generation of a magnetic field due to excited Q-balls. Phys Rev D 58:107301

    Article  Google Scholar 

  • Shiromizu T, Uesugi T, Aoki M (1999) Perturbation analysis of deformed Q-balls and primordial magnetic field. Phys Rev D 59:125010

    Article  MATH  Google Scholar 

  • Skyrme THR (1961) A non-linear field theory. Proc R Soc 260:127

    Article  MathSciNet  MATH  Google Scholar 

  • Skyrme THR (1962) A unified field theory of mesons and baryons. Nucl. Phys 31:556

    Article  MathSciNet  Google Scholar 

  • Smolyakov MN (2018) Perturbations against a Q-ball: charge, energy, and additivity property. Phys Rev D 97:045011

    Article  MathSciNet  Google Scholar 

  • ’t Hooft G (1974) Magnetic monopoles in unified gauge theories. Nucl Phys B 79:276

    Article  MathSciNet  Google Scholar 

  • Tsumagari MI, Copeland EJ, Saffin PM (2008) Some stationary properties of a Q-ball in arbitrary space dimensions. Phys Rev D 78:065021

    Article  Google Scholar 

  • Vasheghani A, Riazi N (1996) Isovector solitons and Maxwell’s equations. Int J Theor Phys 35:587

    Article  MathSciNet  MATH  Google Scholar 

  • Wazwaz AM (2004) The tanh method for traveling wave solutions of nonlinear equations. Appl Math Comput 154:713

    MathSciNet  MATH  Google Scholar 

  • Wazwaz AM (2006) Compactons, solitons and periodic solutions for some forms of nonlinear Klein-Gordon equations. Chaos Solitons Fractals 28:1005

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Persian Gulf University, Bushehr, 75169, Iran

    M. Mohammadi

Authors
  1. M. Mohammadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Mohammadi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohammadi, M. The Role of the Massless Phantom Term in the Stability of a Non-Topological Soliton Solution. Iran J Sci Technol Trans Sci 43, 2627–2634 (2019). https://doi.org/10.1007/s40995-019-00704-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40995-019-00704-6

Keywords

Search

Navigation