A portion of Shemot 15, v. 1-19, known as “Shirat HaYam” (the song of the sea) constitutes the culmination of the weekday section of Pesukei D’Zimra, and is also recited towards the end of this section of prayer on Shabbat and Yom Tov:

1 Then sang Moshe and the children of Israel this song unto the LORD, and spoke, saying: I will sing unto the LORD, for He Is Highly Exalted; the horse and his rider hath He Thrown into the sea. 2 The LORD Is my strength and song, and He Is become my salvation; this Is my God, and I will Glorify Him; my father’s God, and I will Exalt Him. 3 The LORD Is a Man of war, The LORD Is His Name. 4 Pharaoh’s chariots and his host hath He Cast into the sea, and his chosen captains are sunk in the Red Sea. 5 The deeps cover them–they went down into the depths like a stone. 6 Thy Right Hand, O LORD, Glorious in Power, Thy Right Hand, O LORD, Dasheth in pieces the enemy. 7 And in the greatness of Thine Excellency Thou Overthrowest them that rise up against Thee; Thou Sendest forth Thy Wrath, it consumeth them as stubble. 8 And with the blast of Thy Nostrils the waters were piled up–the floods stood upright as a heap; the deeps were congealed in the heart of the sea. 9 The enemy said: I will pursue, I will overtake, I will divide the spoil; my lust shall be satisfied upon them; I will draw my sword, my hand shall destroy them. 10 Thou didst Blow with Thy Wind, the sea covered them; they sank as lead in the mighty waters. 11 Who is like unto Thee, O LORD, among the mighty? Who is like unto Thee, Glorious in Holiness, Fearful in Praises, Doing Wonders? 12 Thou Stretchedst out Thy Right Hand–the earth swallowed them. 13 Thou in Thy Love hast Led the people that Thou hast Redeemed; Thou hast Guided them in Thy Strength to Thy Holy Habitation. 14 The peoples have heard, they tremble; pangs have taken hold on the inhabitants of Philistia. 15 Then were the chiefs of Edom affrighted; the mighty men of Moav, trembling taketh hold upon them; all the inhabitants of Cana’an are melted away. 16 Terror and dread falleth upon them; by the Greatness of Thine Arm they are as still as a stone; till Thy People pass over, O LORD, till the People pass over that Thou hast Gotten. 17 Thou Bringest them in, and Plantest them in the mountain of Thine Inheritance, the place, O LORD, which Thou hast Made for Thee to Dwell in, the Sanctuary, O Lord, which Thy Hands have Established. 18 The LORD shall Reign forever and ever.

(In the liturgy, but not in the Tora:

[the last verse is repeated:]

18 The LORD shall Reign forever and ever.

[and then translated into Aramaic, citing Targum Onkelos:]

HaShem, Malchutai Ka’eim LeOlam U’LeOlmai Olmaya.

[The LORD—His Kingdom is established forever and ever.]

Onkelos consistently avoids anthropomorphisms in his translation/commentary.

In this case, instead of stating that “HaShem” Reigns forever, he explains: HaShem’s “Kingdom” will reign forever.)

19 For the horses of Pharaoh went in with his chariots and with his horsemen into the sea, and the LORD Brought back the waters of the sea upon them; but the children of Israel walked on dry land in the midst of the sea.

In Jewish liturgy, in addition to the repetition of v. 18, and Targum Onkelos’ rendition of this biblical verse, three [four] additional verses are added, each from a different prophet, emphasizing God’s Kingship and/or His Oneness:

(Tehillim 22:29) For the kingship is HaShem’s, and He Rules over nations.

(Ovadya 1:21) And deliverers will go up to Har Tziyon to judge Har Eisav, and the kingdom will be HaShem’s.

(Zecharia 14:9) And HaShem will Be King over the whole earth; on that day HaShem will Be One and His Name One.

(And in your Tora, is written, saying: (Devarim 6:4) Hear, O Israel! The LORD is our God, the LORD Is One.)

(The fourth verse usually is surrounded by round brackets and appears in smaller typeface in most Siddurim, in order to indicate that not everyone recites it at this juncture of the service.)

What might explain these augmentations to “Shirat HaYam”—1) the repetition of v. 18, 2) the addition of the Aramaic translation, and 3) the three [four] verses included at the end of this section?

On the one hand, the addition of these verses reflect a Kabbalistic influence on the prayers. R. Yosef Karo, a distinguished Jewish mystic in his own right, writes in his Halachic commentary “Beit Yosef,” to the Tur Shulchan Orech, Orech Chayim #51:

…Furthermore, in the book Orchot Chayim (#32), concerning the custom of reciting “Shirat HaYam” as part of Pesukei D’Zimra, because it contains “72 letters of holiness” (a reference to the Tetragrammaton) 18 times (aside from verse  17, in which the second reference to God’s Name is written “Alef” “Daled” “Nun” “Yud.” The 18 references are equivalent to 72 (18 x 4 = 72.) However, you will not find them (the 18) in the body of the song, but rather they are in the (additional) verses… Therefore our custom is to recite them at the conclusion of “Shirat HaYam”…[1] And for this reason, it is unnecessary to repeat “The Lord shall Reign forever and ever,” because by doing so you would be adding a 19th Name of HaShem, and )Sanhedrin 29a) “whomever adds, takes away,”

Assuming a Kabbalistic basis for this practice explains why Israeli authorities promote the “Segula” (magical benefits) of reciting “Shirat HaYam” each day: שירת הים – מותאם לסמארטפון. כולל סגולות והסבר – הידברות (hidabroot.org)

… It is written in the Holy Zohar, Parashat BeShalach, #210:

Whomever recites “Shirat HaYam” daily, and understands what s/he is saying, will merit reciting it in the World to Come, to praise with it the King Messiah as the Jewish people rejoice with the Holy One, Blessed Be He. One who does this, the Holy One, Blessed Be He, will Forgive all of his/her transgressions and will Save him/her from all of the troubles that afflict the world.

The Zohar emphasizes that “it is to be recited daily with great joy, comparable to the moment when it was originally said. Its magical powers will then pertain as they did at the first moment,” i.e., when the Song is recited joyously, the Divine Influence from above will be extended like the first moment that it was recited…

However, I believe that the repetition, and addition of verses re Shirat HaYam, can be explained as well without invoking mystical thought. Yael Zigler, in her 2021 essay, “Shirat HaYam: The Triumphant Song of the Sea” Shirat HaYam: The Triumphant Song of the Sea (jewishlink.news) points out that according to Ibn Ezra, “Shirat HaYam” is actually two separate songs, the first describing what has just occurred (Shemot 15:1-11,–v. 19 is a return to the immediate moment)  and the second, projecting years into the future (Ibid 12-8.) There is no question that the people rejoiced over the defeat of their enemies who were intent on injuring, killing, and taking possessions from the Jews. But it would be a substantial error to think that the miracles at the Sea, and, for that matter, the entire Exodus from Egypt, was complete with the final defeat of Phaorah and his armies. God Wished both to give His Tora to His “Am Segula,” as well as Bring them to the Promised Land in which eventually His Temple would stand and He would be worshipped. Ziegler writes:

…(In the second part of the Song, the Jews) glide ineluctably toward Kedusha (Holiness,) a word that also appears at the beginning and end of the song’s second section (in verses 13 and 17). Israel’s future is defined as a journey toward sanctity, which will begin to take shape as the nation enters the Holy land…

The repetition of v. 18, and its Aramaic translation makes clear the emphasis in Shira HaYam that the Jews, in addition to appreciating the past, must look forward to the future as well. But in case for some reason, this is too subtle for some, the addition of three, and perhaps four, verses make such a point that much clearer. The verse from Tehillim stresses that in order for HaShem to “rule,” it will not only be over the Jews, but other nations of the world as well. Ovadia 1:21 states that what will be entailed is an assessment of all of the nations, and those found “wanting” will be expected to “get their acts together.” The verse that is the same as the ending of the well-known prayer “Aleinu,” describes how according to Zecharia, we are looking forward to a time when all will be consistent and in accord with God’s Desires, a theme that is also inherent within Devarim 6:4 (see e.g., RaShI d.h. HaShem Elokeinu HaShem Echad.)

The distinguished historian, Jacob Katz, in his 1984 book, Halacha VeKabbala, explored the extent to which the practices of Orthodox Judaism have been influenced by mysticism. I personally believe that even if that may be so, there are ways to explain certain customs and practices in a manner that they are logically acceptable even to someone who prefers to keep the Zohar at arm’s distance.

[1] שמות (פרשת בשלח) פרק טו פסוק א – יט

(א) אָ֣ז יָשִֽׁיר־מֹשֶׁה֩ וּבְנֵ֨י יִשְׂרָאֵ֜ל אֶת־הַשִּׁירָ֤ה הַזֹּאת֙ 1) לַֽיקֹוָ֔ק וַיֹּאמְר֖וּ לֵאמֹ֑ר אָשִׁ֤ירָה 2) לַֽיקֹוָק֙ כִּֽי־גָאֹ֣ה גָּאָ֔ה ס֥וּס וְרֹכְב֖וֹ רָמָ֥ה בַיָּֽם: (ב) עָזִּ֤י וְזִמְרָת֙ קהּ וַֽיְהִי־לִ֖י לִֽישׁוּעָ֑ה זֶ֤ה  קלִי֙ וְאַנְוֵ֔הוּ אֱלֹקי אָבִ֖י וַאֲרֹמְמֶֽנְהוּ: (ג) 3) יְקֹוָ֖ק אִ֣ישׁ מִלְחָמָ֑ה 4) יְקֹוָ֖ק שְׁמֽוֹ: (ד) מַרְכְּבֹ֥ת פַּרְעֹ֛ה וְחֵיל֖וֹ יָרָ֣ה בַיָּ֑ם וּמִבְחַ֥ר שָֽׁלִשָׁ֖יו טֻבְּע֥וּ בְיַם־סֽוּף: (ה) תְּהֹמֹ֖ת יְכַסְיֻ֑מוּ יָרְד֥וּ בִמְצוֹלֹ֖ת כְּמוֹ־אָֽבֶן:

(ו) יְמִֽינְךָ֣ 5) יְקֹוָ֔ק נֶאְדָּרִ֖י בַּכֹּ֑חַ יְמִֽינְךָ֥ 6) יְקֹוָ֖ק תִּרְעַ֥ץ אוֹיֵֽב: (ז) וּבְרֹ֥ב גְּאוֹנְךָ֖ תַּהֲרֹ֣ס קָמֶ֑יךָ תְּשַׁלַּח֙ חֲרֹ֣נְךָ֔ יֹאכְלֵ֖מוֹ כַּקַּֽשׁ:

(ח) וּבְר֤וּחַ אַפֶּ֙יךָ֙ נֶ֣עֶרְמוּ מַ֔יִם נִצְּב֥וּ כְמוֹ־נֵ֖ד נֹזְלִ֑ים קָֽפְא֥וּ תְהֹמֹ֖ת בְּלֶב־יָֽם: (ט) אָמַ֥ר אוֹיֵ֛ב אֶרְדֹּ֥ף אַשִּׂ֖יג אֲחַלֵּ֣ק שָׁלָ֑ל תִּמְלָאֵ֣מוֹ נַפְשִׁ֔י אָרִ֣יק חַרְבִּ֔י תּוֹרִישֵׁ֖מוֹ יָדִֽי: (י) נָשַׁ֥פְתָּ בְרוּחֲךָ֖ כִּסָּ֣מוֹ יָ֑ם צָֽלֲלוּ֙ כַּֽעוֹפֶ֔רֶת בְּמַ֖יִם אַדִּירִֽים: (יא) מִֽי־כָמֹ֤כָה בָּֽאֵלִם֙ 7) יְקֹוָ֔ק מִ֥י כָּמֹ֖כָה נֶאְדָּ֣ר בַּקֹּ֑דֶשׁ נוֹרָ֥א תְהִלֹּ֖ת עֹ֥שֵׂה פֶֽלֶא: (יב) נָטִ֙יתָ֙ יְמִ֣ינְךָ֔ תִּבְלָעֵ֖מוֹ אָֽרֶץ: (יג) נָחִ֥יתָ בְחַסְדְּךָ֖ עַם־ז֣וּ גָּאָ֑לְתָּ נֵהַ֥לְתָּ בְעָזְּךָ֖ אֶל־נְוֵ֥ה קָדְשֶֽׁךָ: (יד) שָֽׁמְע֥וּ עַמִּ֖ים יִרְגָּז֑וּן חִ֣יל אָחַ֔ז יֹשְׁבֵ֖י פְּלָֽשֶׁת: (טו) אָ֤ז נִבְהֲלוּ֙ אַלּוּפֵ֣י אֱד֔וֹם אֵילֵ֣י מוֹאָ֔ב יֹֽאחֲזֵ֖מוֹ רָ֑עַד נָמֹ֕גוּ כֹּ֖ל יֹשְׁבֵ֥י כְנָֽעַן: (טז) תִּפֹּ֨ל עֲלֵיהֶ֤ם אֵימָ֙תָה֙ וָפַ֔חַד בִּגְדֹ֥ל זְרוֹעֲךָ֖ יִדְּמ֣וּ כָּאָ֑בֶן עַד־יַעֲבֹ֤ר עַמְּךָ֙ 8) יְקֹוָ֔ק עַֽד־יַעֲבֹ֖ר עַם־ז֥וּ קָנִֽיתָ: (יז) תְּבִאֵ֗מוֹ וְתִטָּעֵ֙מוֹ֙ בְּהַ֣ר נַחֲלָֽתְךָ֔ מָכ֧וֹן לְשִׁבְתְּךָ֛ פָּעַ֖לְתָּ 9) יְקֹוָ֑ק מִקְּדָ֕שׁ 10*) אֲדֹנָ֖י כּוֹנְנ֥וּ יָדֶֽיךָ:(יח) 11 ) יְקֹוָ֥ק׀ יִמְלֹ֖ךְ לְעֹלָ֥ם וָעֶֽד   (repetition of this verse throws off the number of Azkarot)   (יט) כִּ֣י בָא֩ ס֨וּס פַּרְעֹ֜ה בְּרִכְבּ֤וֹ וּבְפָרָשָׁיו֙ בַּיָּ֔ם וַיָּ֧שֶׁב 12) יְקֹוָ֛ק עֲלֵהֶ֖ם אֶת־מֵ֣י הַיָּ֑ם וּבְנֵ֧י יִשְׂרָאֵ֛ל הָלְכ֥וּ בַיַּבָּשָׁ֖ה בְּת֥וֹךְ הַיָּֽם: פ

(תהילים כב:כט) כִּ֣י 13) לַ֭יקֹוָק הַמְּלוּכָ֑ה וּ֝מֹשֵׁ֗ל בַּגּוֹיִֽם:

(עובדי’ א:כא) וְעָל֤וּ מֽוֹשִׁעִים֙ בְּהַ֣ר צִיּ֔וֹן לִשְׁפֹּ֖ט אֶת־הַ֣ר עֵשָׂ֑ו וְהָיְתָ֥ה 14) לַֽיקֹוָ֖ק הַמְּלוּכָֽה:

(זכרי’ יד:ט) וְהָיָ֧ה 15) יְקֹוָ֛ק לְמֶ֖לֶךְ עַל־כָּל־הָאָ֑רֶץ בַּיּ֣וֹם הַה֗וּא יִהְיֶ֧ה 16)  יְקֹוָ֛ק אֶחָ֖ד וּשְׁמ֥וֹ אֶחָֽד

(דברים ו:ד) שְׁמַ֖ע יִשְׂרָאֵ֑ל  17)יְקֹוָ֥ק אֱלֹקינוּ 18) יְקֹוָ֥ק׀ אֶחָֽד: