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C"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We consider an extended model with two real scalar fields, <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\phi (x,t)$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03d5<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>x<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>t<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\chi (x,t)$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03c7<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>x<\/mml:mi>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>t<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. The first sector is controlled by the sine-Gordon superpotential, while the second field is submitted to the <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\chi ^4$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>\u03c7<\/mml:mi>\n                    <mml:mn>4<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> one. The fields mutually interact via a nontrivial coupling function <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$f(\\chi )$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>f<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>\u03c7<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> that also changes the kinematics of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\phi $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03d5<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. We briefly review the implementation of the Bogomol\u2019nyi\u2013Prasad\u2013Sommerfield (BPS) prescription (Prasad and Sommerfield in Phy Rev Lett 35:12 1975, Bogomolny in Sov J Nucl Phys 24:449, 1976). We then solve the resulting BPS equations for two different interactions <jats:italic>f<\/jats:italic>. The first one leads to a single kink-kink configuration, while the second one gives rise to a inhomogeneous sine-Gordon kink lattice. We study the linear stability of these new solutions, focusing on their translational modes. We also explore how the strength of the mutual interaction affects the BPS profiles. In particular, we show that a homogeneous lattice with identical kinks is attained in the regime of extremely strong interactions.\n<\/jats:p>","DOI":"10.1140\/epjc\/s10052-025-14211-z","type":"journal-article","created":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T09:50:52Z","timestamp":1746265852000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sine-Gordon kink lattice"],"prefix":"10.1140","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9241-9789","authenticated-orcid":false,"given":"E.","family":"da Hora","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043fhe951","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade Federal do Maranh\u00e3o"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2083-999X","authenticated-orcid":false,"given":"C.","family":"dos Santos","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043pwc612","id-type":"ROR","asserted-by":"publisher"}],"name":"Centro de F\u00edsica e Departamento de F\u00edsica e Astronomia, Faculdade de Ci\u00eancias da Universidade do Porto"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1676-4999","authenticated-orcid":false,"given":"Fabiano C.","family":"Simas","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/043fhe951","id-type":"ROR","asserted-by":"publisher"}],"name":"Universidade Federal do Maranh\u00e3o, Campus Universit\u00e1rio do Bacanga"}]}],"member":"297","published-online":{"date-parts":[[2025,5,3]]},"reference":[{"key":"14211_CR1","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1103\/PhysRevLett.35.760","volume":"35","author":"MK Prasad","year":"1975","unstructured":"M.K. 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